m1Oss7 Sant oh a 36 cats { < its) pte aanety 294 Seas ite tos os Has Dasa 9 Sn sty fe RODE: Hs en Sn ty) en a heats sage A ' bas 6 PE » 3) sedan DEC R aS ppd hetat Hobecate 45) 33 Ses Oe Rian ee) ene bat i Ny Se, m5 = ie Tarecat eres ty) re ataye eesaieody PAs eSB im a ay SED PRD Hr shf ay , ‘ is pet esttae aoe a , iss Shakes aes i {eas : tes { Siiealyeieies 4 Bi sui of 2 SSIES Ante DUAR NR N Maa tne ; tat te i mivtained tet: Age eat toon eacaar dense Diese erty ratte oh tet ae iatinrnas Earn ee : eee esos, an Si OG) 1930 Gift of Elaine Gomberg February, 1984 In Memory of Her Sister Judy Joye @ s¢eS2e700 TOEO O MMM 1OHM/1alN UNDERWATER ACOUSTICS 7 ROPraUODA HATAW. a ie | : a ¢ i i Gy PSO PEEEN AELOUEY MEU Clark Reading Room A Pennsylvania State University Publication ye | UNDERWATER ACOUSTICS Proceedings of an Institute sponsored by the Scientific Affairs Committee of the North Atlantic Treaty Organization and conducted by The Pennsylvania State University at The Imperial College of Science and Technology of The University of London July 31-August 11, 1961 Edited by V. M. ALBERS The Ordnance Research Laboratory The Pennsylvania State University University Park, Pennsylvania SE Distributed by PLENUM PRESS NEW YORK Library of Congress Catalog Card Number 62-8011 ©1963 Pennsylvania State University University Park, State College, Pennsylvania All rights reserved No part of this publication may be reproduced in any form without written permission from the publisher Printed in the United States of America FOREWORD This book represents a compilation of the lectures presented at the Institute on Underwater Acoustics held at the Department of Physics of The Imperial College of Science and Technology of The University of London between July 31 and August 11, 1961. The institute was conducted by the Continuing Education Services of The Pennsylvania State University under a grant from the Scientific Affairs Division of the North Atlantic Treaty Organization. At the institute, eighteen papers were presented by seventeen outstanding scientists in the field of Underwater Acoustics. In addition, eighty-five scientists, representing eleven nations, attended the institute and participated in the dis- cussions following the presentation of each paper. Since each of the lecturers is an authority in his field, these proceedings, which include the bibliographies supplied by the lecturers, should provide a valuable source of information for workers in the field of Underwater Acoustics. The discussions following the lectures, where available, have been included to make these proceedings more meaningful to the reader. Dr. R. W. B. Stephens of The Imperial College, Co-Chairman of the institute, assisted in the preparation of the program and made all arrangements for the lecturers and participants. The contribution of Dr. Stephens in the formulation of the program and in arranging for the housing of both the lecturers and the participants was an important factor in the success of the institute. I wish to thank all of the speakers for their efforts in preparing the lectures as well as for preparing manuscripts in a form suitable for publication. I am grateful to the staff of the Department of Physics of The Imperial College and to the staff of Continuing Education Services at The Pennsylvania State Uni- versity for their assistance in carrying out the program. I am also indebted to Dr. Merritt A. Williamson, Dean of the College of Engineering and Architecture, and Dr. John C. Johnson, Director of the Ordnance Research Laboratory, at The Pennsylvania State University for their support and interest. Vernon M. Albers Chairman Per pepe Ant Miron eyy het nd Slt Ko oii @ at ioe OG TPR ABS ev te geist aie bed peer PS HA. Rt a te | PRP? wih Sb yoriiintsod has ENO Ajo ao” wh yt dasyine® off gpuidence’ wth’ (008% U 209) ry 1 ica G ALLEY shuts fine “lynsey Veh hee yrand |) idea erie ade Py i Sahota age a) 4 ae i at! ipsa Woe Wag aie eae a * ry Hebe REY nit hs ay Ma peabiinos a7 focus A ew 70014 40, Gata | w he yb ad tee at) Gael Syrtitem af) volo .etoiiie fee a Lk) Hab YT) rote. oepign rftine! te) col yimewe aie eee Sati leiG tic n nei ied cals ATEN aaa ay acai 9 ‘itor ¢imae PRO AWVEOT T° AVNER tdodeley fb Atv Be) eee nd rewind, Airolee) hel ako bahia? vin te rae pei ot van! “Adaline iy Pies | MISE TOI Soe 4 WG ,agullo.d Jategenl a!) aoe mh Aas, SBT HH rc ae Ayre big THe Tye wi) | wiereprig ORT lec Ges A! dere 00>) srcatitigacs> aay” iia aeahiae. 2h Bah eayviit Wh diet te quleaon wih ao -plieiedhe wl Fale Wao nt onl Beale Ade AAC ahsugnal ne | Seoul atyyhi rane tal aevolie thats yl al odteate af to Thy tenes eit . a SUAS tO) aldara NTO BW LL WATTS Gee Ty a Se tg sali) Lalo oT io waley4tl Ie leet cial eds be Dere eel ete Lb Otmic “Suvi yao oT te eOuleRSe aallbnid oniunlinod fer Oe Lot bar edi cat mnexgerg wt FeO WAC GL i) boretaeme Tee repens CIO AML we: eat tener yar AY aca dpm rh) ate ith A he sai A Lal ; ft eitsayerd Savona ) webatloa onl) Ts Qe Ge! Cheb a A chap ariae fae gai di)! i: ieee Renta wn i os ro LRP eT) GY Way il breeitigos t OAM Lie j Riat f meee’ Pons + ¥ at —=—gFthat poses : DCT ty a Ge ds ee a ‘ dei Ce as eon eS i Foon ‘tem wl tat Py OSA, Viticn wines fv CONTENTS Introduction Lecture 1 Lecture 2 The Scientific Program Sponsored by NATO HE IR&Bakerwenstoockenorense olerenel« anfaygs asbTarevrench peated TRANSDUCERS DUSchofieldiarr sett te Sos Roe ee ae Gasca eeen sae or lelgaure Ioil listers 65 0 oloo ao G0 OOo COD ODO 1.2 Electroacoustic Conversion Principles ... 1.3 Equivalent Electrical Circuits......... 1.4 Electromechanical Coupling Factor ..... 1.5 Transducer Materials .............. IkGeExamplesiof dransducernsi i) nee ciel IeGoil IPA AeRORES Go G olaoe Ob 0 a 0.614 O blo o ILO IROoweine IRC MENSy G56 45665000000 ee es eo © eo 2 © © © ee ee oe eo ec ee oe 1.6.3 Electromechanical Coupling Coefficient..... 1.6.4 Power-Handling Capabilities ...... 1G) IDAEO Iahyclreop NON 55 56a5000000006 lot Comets Gaclooaagoobo obo odcgces SONAR ARRAYS, SYSTEMS, AND DISPLAYS DiiGauhuekers iis POR Ie I Ee 2.2 Arrays and Directionality............ 2.2.1 Multiplicative Arrays........... 2.2.2 Superdirective Arrays .......... 2.2.3 Multifrequency Two-Element Arrays 2.2.4 Wide-Band Arrays............. Boo) SOWMENe SYSEINS. Goo boaacG 00 b400 50 010 2.3.1 Within-Pulse Scanning Systems Using Multielement Arrays ........... 2.3.2 Within-Pulse Scanning Systems Using Multifrequency Arrays .......... 2.3.3 Double-Transducer FM System .... ZEA DIS PAV SU Meinameinrcs aie erated utet ae omen Seas omens 2.4.1 Integration and Correlation ....... vii oe © ow oONtoauw 10 13 13 13 14 16 20 24 25 29 30 30 32 32 35 37 37 40 A2 43 44 29 Lecture 3 Lecture 4 Lecture 5 2.4.2 Pattern Recognition and Size of Target ..... 2.5 Echo-Formation and Randomization ........... 2.6 Conclusions and Acknowledgments ............ EXPLOSIVE SOURCES DES Westomitcaus:s miouocat ating tone ce oia el arto RE Ee eae ho IBEINETEOUG! ooo dodo oa D0b DO OOD OO KO OUD DDOS 3.3 General Ideas on Scaling Laws and SITSSUIN SHOPS oo oa nado odoD dod do0OG DOOD 3.4 Description of Underwater Explosions.......... 3.5 Measurements and Theory for Underwater EXplOS1ONSi ouster crt oleic etsy ovate site ei aicen in emer eer eueente 3.6 Comparison with Underground Explosions ....... Bol WHOS tin INSTAR GoooooK oD OCD DDO as oOOCS 3.8 Relative Advantages of Underwater lOpagnllosiiom SOWREDS 6500000000 D 0D DoD OOK ODOD Glow) JANG anonleoleimnentS 5 656000dcc0000b50000500 THE IMPROVEMENT OF VIBRATION ISOLATION GEIGS Paar fitter eonSrenoy, tn tac sare ere ts cme me Mee ee Na Al) IDEhanyoybays Ole Shona Ole 5 5560000 d0000000 4.4 Additional Mass in Vibrating Structures ........ Zeb) SMV OTITEU EN / HG Cott OhGioiol wore elnTolbIeIOlcloe alla d/6-0.0 00 6-0 AS OVACKNOWLed sIMeNtS mei ier Ein en nein nnn nnn A SING-AROUND VELOCIMETER FOR MEASURING THE SPEED OF SOUND IN THE SEA M°iGreenspanjandiG|Eqmischieggn-i-)s-) acne caeieaencne Onl) Introduction). cup acdsee ese vey ne MME aCmn ee Osa) Apparatus: \..y step Meme kee NOR Mehetence skewer melicucnonene o-o.l bhewbransducexsvandythesPathirerm eye) ey enirens Boe Wins IMCHROMICS 5 obo oon dnanonoodooc deo .d ce quencys Measure me ntsmem weet Meleledici sie nents Bs JewakorGEN GooodD oo OO DODO DOO DOO ODO OON 574: Stabilitym stiereo crate tore eek tee © . 5.4.1.1 Supply-Voltage and Ambient- Tempers tures hlNctuationSyaem-lene cM-lemenerialiclente Opa leap requencysastabilityaemycl- elena iene: o.422) Calibrations) apelin o00u0g00000000000 5.0 History and Distribution........... Go0n0000 5.6 Acknowledgments ........ god0ddc0b000000 viii 45 46 48 51 51 52 54 57 59 61 64 65 67 68 73 76 83 84 87 87 89 89 92 94 96 96 96 96 96 98 99 67 87 Lecture 6 UNDERWATER SOUND CALIBRATION STATIONS AT LE BRUSC LABORATORY Meupettoocher-ne-ieni cmc: 6.1 Hydrophone Calibration 6.1.1 Electrodynamic C oe es ee ew ee et eh ee ee alibration by Discharge into a Ballistic Galvanometer............ 6.1.2 Absolute Electros tatic Calibration ...... 30 6.1.3 Relative Electrostatic Calibration ........ 6.1.4 Closed-Tank Pressure-Calibration Technique .... see ee eo oe ew ew oe ee ee ee 6.1.5 Calibration by Comparison Using Filtered 6.2 Transducer Calibration 6.2.1 Impedance Measurements .............-. Lecture 7 6.2.2 Principle of the P 6.2.2.1 Separation eo 2 6 © © © © ew 8 © 8 eee ee el Disa Misdnol 55 ooo ooo 006 IDNGRAINES 55500000 Peis G22" PUGS ILGIMNGINs Go ooo bono oo e000 OG BA Aaa IPG INES 4.506050 0d Good 00 0000 6.2.2.4 Size of the Anechoic Tank ..... nite e0 622-20 NSEEUMENtALLON pre eitcleitelicll sie nenellel is) 6.2.3 Application of the Pulse Method for Reciprocity Calibration................ 6.2.3.1 Calibration by Comparison ........ 6.2.3.2 Directivity Measurements ......... 6.2.3.3 Transpare 6.3 Test-and-Calibration B Harbour of Le Brusc . 6.3.1 Mission ...... ncy Measurements....... arge Moored in the 6.3.2 Physical Features and Layout ........... 6.3%3) Electaical Installlationys 5 20) c).se ere «a ele @ 6.3.4 Water Depth... 6.4 Test-and-Calibration B Cag@ullon 6onc00000 arge of the Lake of 6.4.1 Introduction: History ...............4.. 6.4.2 General Descripti 6.4.3 The Test-and-Cal OM obgoo0noc0000000000 ibration Barge.......... 6.4.3.1 General Layout ....... O.oRO) Or OF a lOABIE 6.4.3.2 Mechanica 6.4.3.3 Electrical 1 Operating Gear ........ Installation............ 6.4.3.4 Acoustical Test-and-Calibration Facilities coe eee eo 6 e © © © © © © © 8 oe 8 SOME AREAS IN WHICH UNDERWATER ACOUSTICS RESEARCH IS NEEDED HRSiBakersie esse ee. 7.1 Sound Transducers ix 125 103 125 Lecture 8 Lecture 9 Lecture 10 7.2 PLOPAGAblOny TANS av -jZo/sin Fig. 1.1. Equivalent electrical circuit of a piezoelectric bar. p= _ daw = transformation ratio E si Zo = wt yo/sit = 1/ Yost Bal Co= = LZ capacity of the clamped crystal < where / is the length, w is the width, t is the thickness, d3, is the piezoelectric constant, s¥, is the compliance at constant electric field, p is the density, and «33 is the dielectric constant at constant strain. More complex acoustic oscillators can be analyzed by adding the appropriate acoustic components to the terminals F; and F. In the immediate neighborhood of resonance, a considerably simplified circuit, Fig. 1.2, can be used. Cy) and R are the clamped capacity and resistance; and K, N, S;, and Sp are the motional capacity, inductance, internal loss resistance, and radiation resistance, respec- Fig. 1.2. Simple lumped equivalent electrical circuit of a piezoelectric transducer. SR D. Schofield 9 tively. It is to be noted that in this circuit the motional capacity and inductance are lumped constants while in the mechanical system the stiffness and mass are distributed. The immediately obvious difference is that, whereas the mechanical system can resonate at higher harmonics, the electrical circuit has only one resonant frequency. It is, nevertheless, a very useful circuit for any piezoelec- tric transducer provided attention is limited to the region about the fundamental resonant frequency. Similar equivalent circuits can be developed for transducers based on other force effects. One of the important characteristics of a transducer is the bandwidth. It has become customary to consider two Q factors in transducers: the mechanical or motional Q, Q,, which can be calculated from the mechanical characteristics of the unit or from the motional arm of the equivalent electrical circuit and the electrical Q, Q., which from Fig. 1.2 is w oCS;, where neglecting the dielectric loss resistance $;=S,;+Sr. Q,controls the frequency response in both projecting and receiving modes of operation if either the driver or the receiver has a high impedance. However, in transmission the electrical storage element is usually tuned out and the amplifier approximately matched to the motional resistance. From Fig. 1.2 it can be shown that, parallel-tuning a piezoelectric transducer with an inductance, neglecting the dielectric loss resistance, and matching the impedances of the amplifier and transducer, the bandwidthis given by 2/(0,, + 0.). This quantity is a maximum when 0,,=9,. It will be shown later that the product Qn0- is related to the electromechanical coupling factor, and that for a wide bandwidth a high coupling factor is required. 1.4. ELECTROMECHANICAL COUPLING FACTOR The importance of the ratio of the clamped capacity to motional capacity as a measure of activity in a piezoelectric transducer was first noted by Dye [3] in 1926, but it was not until 1935 that Mason [4] introduced the idea of an electro- mechanical coupling coefficient closely related to this capacitance ratio. Since that time there have been a number of definitions and approaches [1, 2, 3, 6-9] almost all of which were both consistent and correct, but there remained a need for a general definition from which all such definitions could be derived. Hersh [10] presented such a general approach in 1957: if the equations defining a coupled reciprocal system can be written as ¥1= 411 X%1 + 412 X2 (2) Y2= 421 X1 + 222 X2 and are homogeneous in the variables of generalized force and displacement, where the coefficients a,,, are coefficients or ratios of coefficients from the same energy function, the coupling coefficient k of the coupled system is defined by K2= 412 Ga (3) 4i1 422 If the equations of state are mixed in the variables of generalized force and dis- placement, the coupling factor is defined by 412 42 i = —— (4) 441 Ag + 442 Ari ; 10 Lecture 1 The piezoelectric equations of state for the length extensional mode of a bar excited by a transverse field are Si=sh T, + da E3 (5) D3;=d3, 7; + 633E3 When we compare these equations with Eqs. (2), and use Eq. (3), we find that the coupling coefficient is given by the equation diy See (6) E Sir €33 Keo This equation is frequently used to define the electromechanical coupling co- efficient. Starting from Eqs. (2), an expression can be derived for the coupling co- efficient in terms of the input open- (x2 = 0) and short-circuit (y2 = 0) impedances: Zoc —Zsc Zoc [os (7) where the impedances are either all resistances or all reactances of the same sign. Again starting from Eqs. (2), it can be shown that 2 Total energy stored unclamped (x2 = 0) — Total energy stored clamped (y = 0) RO = Se ee Total energy stored unclamped (x2 = 0) In the case of a piezoelectric transducer, this is equivalent to x2 — Energy stored in mechanical form (9) Total electrical energy input Using the simple lumped equivalent circuit, Fig. 1.2, the electromechanical coupling coefficient derived from Eq. (7) reduces to k2 = K ~T OAK (10) However, since the equivalent circuit of Fig. 1.2 is not exact, k, is not the true electromechanical coupling factor. It can be shown that for a longitudinally resonant piezoelectric bar 2 a 11 7?/8 — k? (n?/8 — 1) OM A useful approximation in transducer design is reel — )= 0m. (12) and hence, it can be seen from the previous section, the tuned bandwidth is de- pendent upon the coupling factor. 1.5. TRANSDUCER MATERIALS Although some use has been made of the electrodynamic and Vy effects in transducers, most underwater acoustic units have made use of the piezoelectric, D. Schofield 11 TABLE 1. I d-10%,| g-10%, 2 el legas ie one . 11 23 58 28 24 177 38 16 175 : tan 6 at Material Ole om Quartz, X-cut ADP 45°Z Lithium sulphate Rochelle salt 45° X-cut BaCaTiO, >0.10 BaCaCoTiO3-NRE 4 0.02 PZT-4* 0.02 PZT-5* 0.11 Pb(NbOs)2 electrostriction, or magnetostriction phenomena. The most important character - istics for transducer applications of piezoelectric, polarized electrostrictive, and magnetostrictive materials are summarized in Tables 1.] and 1.1]. The relative importance of the various material parameters depends upon the particular re- quirement of the transducer incorporating the material, but the parameters presented do indicate some of the advantages and disadvantages of the various materials. Furthermore, since the materials are not isotropic, the magnitude of the parameters depends upon the mode of operation: e.g., the piezoelectric con- stants depend onthe cut ofthe sample and the coupling factor changes for different modes of vibration. Undoubtedly the most important single characteristic of a transducer ma- terial is the electromechanical coupling factor. It has already been shown that the coupling factor is related to the ratio of stored mechanical energy to total electrical input energy for electrical to mechanical conversion and that it con-~ trols the maximum bandwidth of a projector. In addition, Kendig [11] recently emphasized that for detecting very small acoustic signals, it is the equivalent noise pressure of the receiver that is of prime importance, not the sensitivity of the hydrophone. He developed expressions for the efficiency and equivalent noise pressure of three different shapes of hydrophones, and k*/tan 6, in which 6 is the dielectric loss angle, is a common factor in each equation. Thus, k?/tan 5 appears to be a good criterion for hydrophone materials. This factor is TABLE 2.1 Material Nickel Polarized Remanent 7-108 2 V Permendur | Remanent 8.5-1078 13 Alfer Polarized 9-107 4% Co-Ni Polarized 10,3:107* Ferroxcube A Remanent 12 Lecture 1] highest for the ferroelectric ceramics, particularly PZT-4, and for quartz. However, with low-dielectric-constant materials such as quartz, the shunting effect of even short lengths of cable significantly reduces the effective sensi- tivity of the unit. Care should be exercised in the use of any simple criterion such as k?/tan§; in practical cases the whole receiving and recording system must be considered. For projectors againthe coupling factor andtan §, particularly at high driving fields, are important. In addition, it is desirableto have a low-impedance device to avoid high voltages, and this is achieved by using high-dielectric-constant materials. With quartz, the impedance of the units is so high that voltage break- down across the crystal surfaces limits the power output. The most interesting materials for high-power projectors are PZT-4 and the cobalt additive barium titanate, NRE-4 [12]. Among the other properties which affect the choice of ma- terial are the mechanical strength, the aging of the parameters, the variation of parameters with temperature, and the maximum temperature at which the ma- terial can be used. There is one big difference between the crystal piezoelectric materials and the ceramic pseudopiezoelectric materials. Because of the crystalline nature of the former, the impurities are small and the values of the parameters are reasonably constant and subject to little modification. The ceramics are not pure materials, and compositions consisting of mixtures of chemical compounds have been developed with particular characteristics. Small percentages of additives can have a pronounced effect on some characteristics. For example, Fig. 1.3 shows the effect of adding small quantities of cobalt to a barium titanate com- position on the dielectric loss tangent as a function of exciting field. A corollary is, of course, that small changes incompositionand manufacturing technique can have large effects on the material parameters. Reproducibility on a production scale has presented problems with some compositions. Some characteristics of the more important magnetostrictive transducer materials are given in Table 1.II. Only the 4% cobalt—nickel alloy [13] has a cou- pling coefficient comparable with the coupling factors of the ferroelectric ceramics. With the exception of the ferrites, the main advantage of the mag- netostriction unit is ruggedness. It is a low-impedance device and there are Fig. 1.3. Tan § vs ac field for barium-calcium titanate with additions of cobalt. DIELECTRIC LOSS TANGENT {e) 0.5 1.0 15 2.0 2.5 3.0 3.5 4.0 A.C. FIELD, KV/cm D. Schofield 13 no insulation problems; it does not have tobe enclosed in a watertight container. The disadvantages are that the unit, if made of metal, must be laminated to keep the eddy-current loss low, and this affects the useful top frequency (about 50 keps); for optimum operation magnetostrictive materials require a bias field, necessitating an auxiliary magnetic circuit. 1.6. EXAMPLES OF TRANSDUCERS The remainder of the paper will be devoted to a consideration of two typical transducer designs: the first is a design of a high-power projector, the basic ideas of which can be used from a few kcps to over 100 kcps; the second is a hydrophone for operation deep in the ocean. 1.6.1. Projectors Simple resonant bars do not have optimum characteristics for projectors. For example, the mechanical Q of a longitudinal resonant bar of barium titanate radiating into water is about 50; whereas for the maximum bandwidth condition (0.%0,) and with a coupling factor of 0.2, 0, should be 5. A more complex acoustic oscillator design has a larger number of variables with which to achieve the required characteristics. 1.6.2. Resonant Frequency Consider an idealized compound-bar resonator [14,15], of the type shown in Fig. 1.4. The center of the ceramic sectionis a velocity node and each half of the element may be considered separately as a quarter-wave vibrator, the head being 3-ply and the tail 2-ply. By setting up the equations of the dynamic dis- placements in the various plys of the element and substituting the various bound- ary conditions at the interfaces, the conditions for resonance can be determined. For the 3-ply vibrator we have 234s D LIES 5 5 AED oo ai (13) Z2A2 ZA, ZA, where Z=p,c, is the characteristic impedance; p; is the density of the ply 7; c, is the velocity of sound in plyi; t; =tank,l, ; k, is the wave number of ply i 1 is the length of the ply7; and a is the cross-section area of plyi. If 13 KA3, tan k3l3 ~k3l3 and Z3A3t3=@M, where M is the mass of section 3. CERAMIC SANOWICH SS HEAD MASS “A WHY Fig. 1.4. Compound-bar piezoelectric element. |e — HEAD SHANK ar ans 5 —l TAIL 14 Lecture ] Also, A, =A. and Eq. (13) simplifies to @Ul ty, ONG AD 5 (14) Z2A2 ZA Zi For the tail section the condition for resonance is 7; tats 4 1.6.3, Electromechanical Coupling Coefficient An expression for the coupling factor of a compound bar can be developed by considering the complete equivalent circuit and using Eq. (7). For the resona- tor in Fig. 1.4 in which /; =1,, the expression [16] is 2 Ke se Tass , lad 53, Tess 1 DNS,” MZ Gy DlSs where k is the coupling coefficient of the active material alone and s, is the compliance of the ith ply. The significance of the various material parameters can be more easily appreciated by simplifying the compound vibrator so that the front and back masses are of the same material and are of the same diam- eter as the active component, Equation (15) reduces to 2 A: lates eee NY 2th ees SS Tae Cafolln = noe (16) where /; is the total length of the element. Equation (16) shows that for a high coupling coefficient, the compliance of the loading mass should be small compared with the compliance of the active ma- terial. The theoretical and experimental variations of coupling factor with the ratio of active length to total length of the vibrator are shown in Fig. 1.5. The agreement between the experimental points (whichare fora brass-loaded barium titanate sandwich) and theory is good. , -50 | z ua oO z -40 =| uw Ww ° © .30 4 (o) = & .20 4 me aye a BaT + BRASS Fig. 1.5. Variation of coupling co- 8 ——— Rata efficient with the ratio of active to "10 inactive length for a compound-bar = element. te} 2 4 -6 8 1.0 e ACTIVE LENGTH ! TOTAL LENGTH D. Schofield 15 It has already been stated that for maximum bandwidth the practical problem is to achieve the condition 0,,~0, . Themechanical 0 can be calculated from the equation _ Wo Me 2 (17) where M, is the effective mass of the element and can be calculated from kinetic energy considerations, poc, is the characteristic impedance of sea water, 4 is the effective radiating area, and wo is the resonant angular frequency. There should also be an additional small term in the denominator to take into account the internal mechanical losses in the transducer element. With this type of ele- ment there are alarge number of possible variables with which to obtain optimum characteristics for the particular requirement. The mechanical Q can be adjusted by altering the effective mass or the acoustic loading. It is usually easier to adjust the acoustic loading by changing the radiating area of the head. In a projector, only the behavior in the neighborhood of resonance is usually important, and it is a simple matter using the foregoing equations to predict the lumped equivalent circuit when the electrostatic capacity is specified. Although the compound-bar transducer has been described in terms of a mass-loaded piezoelectric element, a very similar analysis canbe carried out for longitudinal mass-loaded magnetostriction units. Figure 1.6 is a photograph of four barium titanate mass-loaded compound elements ranging in resonant frequency from 120 kcpsto 5 kcps. The construction is similar in all cases: a barium titanate sandwich loaded with a head and a tail. Fig. 1.6. Typical transducer elements. 16 Lecture ] All but the 120 kcps unit have aluminum heads with a head-to-shank area ratio of 4 to 1 and a brass tail. The components of an individual unit are cemented to- gether with a strong epoxy adhesive, electrical contact being made to the elec- trodes of the barium titanate discs by copper gauze in the joints. The elements are usually mounted in air-filledcases, radiation being admitted through a neoprene window which has the same characteristic impedance as sea water and is bonded to the radiating surface of the heads. Figure 1.7 is a typical box and Fig. 1.8 shows an array of boxes in a towed body for use in propagation studies. The calibration results of a 4-element, 5-kcps transducer having a radiating area of about one wavelength by one wavelength are shown in Fig. 1.9. 1.6.4. Power-Handling Capabilities Transducers such as the ones just described are capable of radiating powers of several watts per square centimeter of radiating area, and with the develop- ment of such projectors the factors which limit the power-handling capabilities of transducers become important. The onset of cavitation determines the limit imposed by the medium, i.e., the maximum power that can be transmitted by a projector of a certain radiating area. Cavitation occurs when the instantaneous acoustic pressure exceeds the sum of the static pressure and any inherent cohesive pressure of the liquid. Under this condition small cavities filled with water vapor are formed. When applied to transducers cavitation can be described physically as the rupture of the water in front of the projector face caused by the negative-pressure excur- sions exceeding the sum of the hydrostatic pressure and the tensile strength of Fig. 1.7. Five-kcps trans- ducer. D. Schofield 17 Fig. 1.8. Array of 5-kcps transducers, the water. The presence of these cavities or bubbles sets an upper limit to the power transferred from a vibrating piston tothe water since they reflect, scatter, and absorb the incident energy. At the same time, the radiation resistance changes and the acoustic waveform is distorted. The latter occurs because the amplitude of the acoustic signal is not symmetrical about the zero axis and a form of rectification takes place. Considerable erosion of the transducer face can occur. _ Assuming that water does not exhibit a cohesive force and equating the atmos- pheric pressure to the peak acoustic pressure, we find that the intensity to pro- duce cavitation at shallow depths is 0.3 w/cm?. As is well known, a sound intensity R= 313002 fo Qm Fig. 1.9. Calibration results k of 5-kcps transducer. PRO SENS fo H/P SENS fo Nea ma = K=.00183 pf N=520mh Sw=34102 S| = 340 5.1 KC/S 4.9 0.17 217 #BAR/ VOLT AT 3° 370 4 VOLT/ p» BAR 81% 90% 18 Lecture 1 of about 1 w/em? is required to produce cavitation in sea water. This implies that the inherent tensile strength of sea water is about 0.8 atm. The relationship be- tween intensity to produce cavitation I (w /cm*) and the depth of the projector in feet H is therefore of the type ts 03(4 + 1.8) (18) If such a relation is reliable, the cavitation limit is raised to about 7 w/cm? at a depth of 100 ft. No published work on the effect of depth or hydrostatic pressure on the cavitation limit has been found; however, the limit of 7 w/em? at 100 ft is in agreement with measurements carried out by the Naval Research Estab- lishment which will be described later. The above discussion of cavitation has been oversimplified; the presence of dissolved gases, impurity nuclei, temperature, andthe pulse length of the acoustic signal will all affect the intensity at which cavitation is initiated. The radiating face of the transducer can also affect the inception of cavitation and “hot spots" can occur at levels considerably below the average level of cavitation. Further studies on cavitation as applied to transducers are desirable. Although cavitation is the ultimate factor limiting the power output, many transducers reach their maximum power-handling capacity before the onset of Cavitation even at shallow depths. Crystal piezoelectric transducers of the ADP and quartz type are inherently high-impedance devices requiring very high voltages to excite them to high powers. The limiting factor in this class of trans- ducers is not cavitation but the voltage at which breakdown occurs across the sur- face of the crystals. The important factors in the barium titanate compound-bar type of element are considered to be: (a) the dynamic strength of the element and (b) the heating associated with the dielectric and mechanical losses. The dielectric losses are kept as low as possible by using a specially developed barium titanate composi- tion with additions of cobalt [12]. The mechanical losses are not a problem since the elements have a high motional-to-acoustic conversion efficiency. The power- handling capacity therefore appears to be limited by the dynamic strength of the element. Tests were carried out on a 10-kcps transducer containing four elements at a depth of about 100 ft with 75-msec sinusoidal pulses at a repetition rate of 1 per sec. Figures 1.10 and 1.11 and Table 1.1JI summarize the results. It is evi- dent that the change in admittance and the decrease in efficiency is due to an in- crease in the internal mechanical losses. An examination of the conductance vs frequency curves shows that the clamped value of conductance, which is propor- tional to dielectric loss, changes little with increasing driving voltage as was expected with the barium titanate composition used. The elements fractured at about 6 w/cm?, It can be readily calculated that at this peak power output, the stress at the node is about 670 psi. Tensile-strength tests showed that the static strength was about 3000 psi or four times the dynamic strength. This discrepancy has never been satisfactorily explained. Care was taken to eliminate transients, and fatigue is not a satisfactory explanation since one pulse at the high level would cause the element to break. The fracture took D. Schofield T T 7 Tar nramea T Teareneal 1.3 >I ° 50 V 1.1 a 400V | n 8 & 1350V =x Z9 4 4 = = =7 | uu oO = &.5 | c) 2 g Oo 3 a 4 Fig. 1.10. Conductance vs Me frequency for various ex- citing voltages. all — lL -__s! _L gered 5 6 7 8 9 10 Th 12 13 FREQUENCY KC/S T T Vv T T T {0 N = WATTS /CM@ OF RADIATING FACE °o 100 18 8 ° oS r & 5 2 80 | 6 Ww 4 : : & 60 449 WwW ps z Fig. 1.11. Power output and 40 7 25 efficiency vs input power. EFFICIENCY a [o} -4 8 1.2 1.6 2.0 2.4 INPUT POWER (KW) TABLE 3. Ill Driving voltage rms volts Quantity Resonant frequency, f 9 : Mechanical Q 5.5 Coupling factor 0,22 Clamped capacity 0.072 Clamped resistance ohms 12,500 11,200 10,000 Motional capacity, K put 2,680 3,050 3,700 Motional inductance, N mH 107.1 96.5 81.0 Motional resistance, Sy ohms 1,150 970 850 Radiation resistance, Sy ohms 7125 573 430 Internal loss resistance, s, ohms 425 397 420 Projector sensitivity at 3 ft pbar/yv 332 320 322 Over-all conversion efficiency, neg To 59 54 47 Motional to acoustic conversion efficiency, 7 ma To 63 59 51 20 Lecture ] place either in the barium titanate or inthe joints. Since with present techniques the joint strength can be made at least equal to the tensile strength of the barium titanate ceramic and since it is unlikely that the strength of the ceramic can be increased significantly, a method was sought which would overcome the inherent tensile weakness of the elements. Use was made of the high compressive strength of ceramics: a mechanical bias or compressional prestressing was applied to the ceramic sandwich so that the dynamic tensile forces would be eliminated or at least held within the dynamic tensile strength of the ceramic [17]. Figure 1.12 is a cross-section sketch of a typical element. The stress is applied by means ofa bolt which passes through a hole along the center line of the element and is threaded into a tapped hole in the head piece. The bolt is then tightened with a torque wrench to apply compressional stress to the ceramic. Calibration of stress-rod elements showed that the introduction of the stress - rod had little effect on the performance of the elements; the electroacoustic efficiency remains sensibly the same regardless of stress. Power outputs of 7 w/cm? were achieved but tests at higher powers were eliminated by the incep- tion of cavitation. Driving these units ina highly cavitating state at shallow depths or in air did not change their characteristics. The principles of prestressing are, of course, applicable to any transducer in which the amplitude of vibration of the element is limited by the mechanical strength of the active material or by the joint strength. Since all ferroelectric ceramics and magnetostrictive ferrite ceramics are weak intension but inherently strong in compression, prestressing should allow transducers to be built with higher power-handling capability and with greater resistance to mechanical shock. 1.6.5. Deep Hydrophones To illustrate the problems associated with the design of transducers for operation at great depths, a hydrophone designed to operate at depths down to 15,000 ft will be described. The first requirement of a deep transducer is that it be mechanically capable of withstanding the hydrostatic pressure. A spherical shell is an excellent shape to withstand hydrostatic pressure since the stress is evenly distributed and no stress concentrations occur. Consider a thin spherical shell of a ferroelectric material which is polarized in the radial thickness. The low-frequency sensitivity of the unit is given by VE tes Dees N=m=p) Gn Gs p+ o) (19) P aaa ees Be . | NODAL PLATE STRESS BOLT Fig. 1.12. Sketch of stress-rod element. HEAD ee TAIL D. Schofield 21 where p = a/b and a and b are the internal and external radii of the shell, respec- tively. For a thin shell p +1 and the equation reduces to —=-b §3 The sensitivity of a thin spherical-shell hydrophone is therefore directly pro- portional to the diameter. The sensitivity as a function of frequency should be constant until the sphere is no longer a small fraction of a wavelength, say \/8. When this occurs, there will be a phase difference across the sphere and cancellation will cause a reduc - tion in the sensitivity. Resonance occurs in air at a frequency given by vesall eel (20) 7b | 2p (1 - 0) where Y,, is the elastic-stiffness constant, o is the Poisson ratio, andp is the density of ceramic. Only for very thin-walled spherical shells is the resonant frequency appreciably lower in water than in air. Spherical shells have been assembled by cementing together carefully selected hemispheres with a nonconducting adhesive such as an epoxy resin. The lead to the inner electrode passes through a ceramic-to-metal seal in the shell. The hydrophone is waterproofed by several dippings in a liquid neoprene solution. The sensitivity as a function of frequency is given in Fig. 1.13 for a 3-in. diameter 1) -in. wall thickness barium titanate sphere. The experimental sensi- tivity is in good agreement with the theoretical value of 17 pvolt/ubar. As suggested previously, the sensitivity is flat with frequency until the sphere is about A/8, i.e., at about 3 kcps. Theoretically, a spherical transducer should be omnidirectional at all frequencies but, since the practical units are not perfect spheres, deviations from true omnidirectionality occur in the neighborhood of resonance and at higher frequencies. At resonance the directivity pattern is omni- directional to about 1 db and at 50 kcps to about + 2 db. 100 T a mmnns T i amrnan T a 1 jaan pt VOLTS /2 BAR 10 FREQUENCY KC/S Fig. 1.13. Hydrophone sensitivity vs frequency for a 3-in. diameter and V4-in, wall barium titanate sphere. 22 Lecture ] [4 +20 T T T r u r u u Fig. 1.14. Sensitivity at 200 Loe> Gee Se < == = cps vs hydrostatic pressure. 18 5 2ND cycLe 16 |= i —————— {a ° | 2 3 4 5 6 7 8 PRESSURE (10° PS1) Figures 1.14 and 1.15 show the effect of pressure on the sensitivities of a barium titanate and a PZT-4 spherical hydrophone at 200 cps for the first and second cycles of pressure; there is little change in the barium titanate but the sensitivity of the PZT-4 unit is reduced from approximately 24uvolts/ubar to 20pvolts /ubar. Very little work has been published onthe effect of pressure on the important parameters of transducer materials. However, some work has been published on the effect of stress on the dielectric properties of ceramic ferroelectrics [18] and it has been shown that large changes in dielectric constant can occur. The effect of stress is complicated; and the results depend on a number of variables in addition to the stress; the state of polarization of the samples, their history, time of measurement after the application of stress, and whether the stress is unidimensional, planar, or hydrostatic. These facts probably account for some of the disagreement among the papers. 26 22 ST CYCLE | n n }# VOLTS / & BAR n > Fig. 1.15. Sensitivity at 200 cps vs hydrostatic pressure call of PZT-4 sphere. 2ND cycLe PRESSURE (10> PS!) D. Schofield 23 DIELECTRIC CONSTANT “/e, (10%) Fig. 1.16. Variation of dielectric constant with hydrostatic pressure. ie) 2 4 6 8 10 12 PRESSURE (10°PS1) Barium titanate has atetragonal structure, the elongatedaxis being the direc- tion of polarization. The application of planar compressional stress to ceramic barium titanate tends to align the elongated axis, or c axis, normal to the plane of the stress. Since the intrinsic permittivity is considerably smaller along the c axis, than in the adirection,this domain alignment should result in a reduction of the contribution to the total dielectric constant from the intrinsic permittivity of the domains. There are other contributions tothe total dielectric constant (see [18]), but this is sufficient to illustrate one effect of stress and to suggest that other parameters of the materials may also be affected. Figure 1.16 shows the LL LL LL} DIELECTRIC CONSTANT K fo) ) 3 fo) ° fo) = nN ol > fo} °o fo) fo} fo} o o fe) 0.1 ! 10 100 TIME (MINUTES) Fig. 1.17. Aging of dielectric constant following application of 9000 psi to a barium titanate sphere. 24 Lecture 1 | effect of pressure on the dielectric constant of 3-in. diameter, '/-in. wall thick- ness spheres of barium titanate and PZT-4, Each experimental point was taken 10 min after the application of stress. In additionto the pressure effect, there is a time effect shown in Fig. 1.17. The capacity decays linearly with the logarithm of time after the application of the stress. This is an aging phenomenon similar to the aging obtained following the poling of ferroelectric ceramics. Figure 1.18 shows the effect of pressure on the dielectric constant, with d constant and the coupling coefficient of NRE-4 (BaCaCoTi0s); the material was in the form of a 3-in.-diameter, '/,-in.-wall thickness sphere. It should be emphasized that all the parameters (e.g., dielectric constant, coupling), need to be examined when considering the effect of pressure on trans ~ ducers. It should also be noted that these results are only applicable to trans - ducers subjected to two-dimensional stresses, the components of which are approximately equal. 1.7. CONCLUSION It has not been possible to cover even superficially the whole of the field of electroacoustic transducers and no attempt has been made to do so. High-power projectors, highly efficient over a relatively narrow bandwidth, can be designed for the frequency region of a few kcps to over 100 kcps. These longitudinally resonant projectors are not satisfactory at low frequencies, say less than 1 kcps, because of their physical size and consequent difficulties in handling. Flexural resonances and designs incorporating relatively soft mechanical springs can be used and are effective in reducing the physical size. However, low-frequency Projectors, particularly for deep operation, remain a problem. Hydrophones for particular applications at shallow depth are fairly readily designed. Both projectors and hydrophones for operation at great depth present inter- esting problems. At N.R.E. a study has been undertaken of the effect of stresses, unidirectional, bidirectional, andthree-dimensional, onthe parameters of ceramic = “ T T T T T T T T i 60 , Bike nu = | Fig. 1.18. Variation of die- — = ~= ~_ lectric constant, piezoelec- 0 tric constant, and planar = 50 1 1 1 i i , ns ; rs) coupling coefficient with hy- drostatic pressure for NRE- 4 in the form of a 3-in.-di- 35 ameter sphere. it ESE | fo) I 2 3 4 5 6 7 8 PRESSURE (102 PS!) D. Schofield 25 ferroelectric transducer materials. Not only will information pertinent to the design of transducers be produced, but also data which must be explained by any comprehensive theory of ferroelectricity. To date great use has been made ofpressure release materials, e.g., sponge rubber, or air, in transducers. These conventional pressure-release materials are not suitable for use at great depths: sponge rubber collapses and the use of air requires cases which are mechanically very strong, and hence heavy and bulky. It may, of course, be possible to design elements which will only radiate unidirectionally. Techniques using spatially separated units and time delays can be used to obtain unidirectional hydrophone arrays. Knowledge of cavitation applicable to transducers is limitedand further work is desirable. Although in the past decade with the introduction of ferroelectric ceramics, there has been much improvement intransducer materials, further improvements in coupling factor and loss are desirable. 1.8. ACKNOWLEDGMENT This work is published by permission of the Defence Research Board. DISCUSSION DR. W.N. ENGLISH asked the lecturer how closely the performance of a low- frequency transducer followed the design performance figures and, secondly, whether the production of a transducer operating at 1 to 2 kcps and giving, say, 110 db above 1d/cm” at 1 yard was now feasible without having a weight of several tons. DR. SCHOFIELD: The physical principles of low-frequency transducers are the same as for transducers at high frequencies. Therefore, provided that all the important parameters are taken into account, the design performance of low- frequency transducers can be predicted to the same order of accuracy as trans- ducers at higher frequencies. Low-frequency resonant projectors are large and heavy for two reasons: 1. Low-frequency mechanically resonant systems are inherently larger than for frequencies in the range of tens of kilocycles 2. To obtain a good transfer of energy from a vibrating piston to the water, the dimensions of the radiating face must be at least the order of one wavelength For a highly efficient projector at 1 kcps, the dimensions of the radiating face must be abuut 5 ft. To keep the weight of the projector low, care must be taken in designing the mechanically resonant system, and some compromise in characteristics such as frequency bandwidth and depth of operation may be necessary. I think that a 1 keps projector with a weight of less than one ton is practical. DR. S. WENNERBERG suggested that the reduction of the dynamic tensile strength in a composite transducer could originate inthe excess stresses caused by differences between the Poisson coefficient of the different materials, and inquired whether any investigation had been made of this possibility. 26 Lecture 1 DR. SCHOFIELD: No investigations into this possibility have been made. PROFESSOR R.E.H. RASMUSSEN referred to a formula quoted by Dr. Schofield giving the maximum intensity of radiation (/, in w per square centi- meter) from a barium titanate transducer interms of the depth (H) of immersion in feet, when cavitation is the limiting restriction as !=0.3 (H/32 + 1.8)?. DR. SCHOFIELD: This formula should only be usedasa "rule-of-thumb" indi- cation of the cavitation level. The presence of dissolved gases and impurity nuclei could cause large deviations from the levels predicted by this formula. MR. J.S.M. RUSBY commented that the pattern of cavitation observed on the radiating face of the 10-kcps longitudinal projector mentioned in the lecture could result from the regional lines of high displacement arising from flexural vibrations, and so lowering the cavitation threshold as was observed. He also enlarged upon the suggestion concerning planar arrays of projectors in which it was stated that a method of overcoming the pressure-release problem in deep water was to make the rear ends of the individual elements inefficient as radia- tors compared with their front faces. Mr. Rusby said that this could be achieved by reducing the cross-sectional areas of the rear ends and separating them; in this way, the value of the total radiation impedance as seen by the rear of the array would be lowered. DR. SCHOFIELD: It is agreed that the cavitation erosion marks could be caused by "flapping" of the radiation heads. NRE have been considering methods of mismatching the tails of elements to water as a means of reducing back radiation. DR. H. A.J. RYNJA following upon a point raised in the discussion of low- frequency transducers on the use of magnetostrictive devices, spoke of his own experience with a scroll of 1m diameter of a nickel—four-percent cobalt ma- terial forming a resonator of 1.5 kcps with a tuned bandwidth of one octave, With two such rings mounted coaxially and driven with 90° phase difference and with pressure-release material on the outside surface of the rings, he had suc- ceeded in obtaining quite sufficient power in unidirectional radiation. Dr. Rynja agreed, however, with Dr. Schofield on the difficulties of manufacturing the scrolls. REFERENCES 1. F.A. Fischer, Fundamentals of Electroacoustics (Interscience Publishers Inc., New York, 1955). 2. W. P. Mason, Electromechanical Transducers and Wave Filters (D. Van NostrandCo. Ltd., 1942, 1948). 3. D.W. Dye, "The Piezoelectric Quartz Resonator and Its Equivalent Electrical Circuit,” Proc. Phys. Soc., Vol. 38, 339-457 (1926), 4, W. P. Mason, "An Electromechanical Representation of a Piezoelectric Crystal Used as a Transducer," Proc, Inst. Radio Eng., Vol. 23, 1252-1263 (i935). 5. W. P. Mason, Piezoelectric Crystals and Their Applications to Ultrasonics (D. Van Nostrand Co. Ltd., 1950). 6. P. Vigoureux and C. F. Booth, Quartz Vibrators (H M. Stationery Office, 1950). 7. H. Hecht, Die Elektroakustischen Wandler (Johann Ambrosius Barth, Leipzig, 1954), 8. F. V. Hunt, Electroacoustics (Harvard Univ. Press, 1954). D. Schofield 27 9. R. Beckmann, "Some Applications of the Linear Equations of State," Trans. Inst. Radio Eng. PGUE, Vol. 3, 43-62 (1955), 10, J. F. Hersh, "Coupling Coefficients," Acoustics Research Lab. Harvard, Tech. Memorandum No, 40. 11, P.M. Kendig, J. Acoust. Soc. of America, Vol. 33, 674-676 (1961). 12. D, Schofield and R. F. Brown, Can. J. of Phys., Vol. 35, 594-607 (1957). 13. C. A. Clark, Brt. J. of Applied Physics, Vol. 7, 356-360 (1956). 14, Kinsler and Frey, Fundamentals of Acoustics, Chapter 3 (1950). 15. H. Nodtvedt, Electromechanical Analogues Applied to Magnetostrictive Systems, Forsvarets Forkning- sinstitutt Arbok (1947), In English. 16, A. Mohammed (unpublished work), 17. R. F. Brown (unpublished work). 18. R. F. Brown, Can. J. of Phys., Vol. 39, 741-753 (1961). (Contains list of references on the effect of two-dimensional stress on the dielectric constant of ferroelectrics.) - Bety ‘ ¥ Us fl] i sk i aa 7 Vy ; ea Miva ADOT SAG 1 ean al oni ital vi vad Saati ty B24 nT i) on ray vey, a ; SAC) ' Po it ~ ‘a ap, es ‘ : 7 lal Roky a ' Sata a ke Ren ee mie b Tee: pind ves vmeoulierta i vat eas “e sienna a hes a? 4 Haas FA was Pa slay ie fe toga pe Rats ite alan io wlth wait REL HHA eS eee ys Sry Qaeartty = hy'e® pane 7 Le é a wet a. LECTURE 2 SONAR ARRAYS, SYSTEMS, AND DISPLAYS D.G. Tucker Department of Electrical Engineering University of Birmingham Birmingham, England 2.1. INTRODUCTION The echo-location group of the University of Birmingham has been concerned primarily with active sonar systems. Apart from general considerations of long ranges and oceanic propagation (with which we are not able to deal) it has seemed to us that the main directions in which sonar research must progress are: 1. The gathering of more information about what lies within the area of search, and 2. The processing and presentation of this information sothat classification of targets is quick and reliable. The more progress that is made with 1, the more difficult quick classification becomes, since with a human operator the sorting out of the increased informa - tion becomes too large a task for immediate visual decision. Yet without the increased information, the process could not possibly become more reliable. It is not possible to separate completely these two lines of work, 1 and 2, and a coordinated approach to them is the one which is most likely to succeed. To gather more information about what lies within the area of search, it is necessary to achieve one or more of the following: (a) higher directionality and (b) higher range resolution to give geometrical information—shape and size of targets; (c) knowledge of frequency response of targets; and (d) more rapid scanning. The direct approach to (a) is to use larger transducer arrays, but, like many other people, we have been looking closely into the possibilities of obtaining higher directionality from a given size of array by such methods as superdirec- tivity, multiplicative processing, multifrequency operation, and double-FM oper- ation. The last two methods, together with (b) and (c) above, demand the use of wider frequency bands in the water, andso we have had to think about both trans - ducers and arrays suitable for operation over a wide frequency band. The need for more rapid scanning is not only obvious in itself, but follows more emphati- cally from (a); and we have therefore done a great deal of work on the develop- ment of within-pulse electronic scanning systems. 29 30 Lecture 2 The approach to quick and reliable classification is not so obvious. The combination of (a), (b), and (d) above evidently gives rise to the possibility of an accurately delineated visual display of target shape; but in typical operational situations the ratio of the number of unwanted (or irrelevant) targets to the number of wanted targets is so large that the human task becomes too great, and reliability suffers. In the corresponding radar case, this ratio is, in con- trast, usually very small, and automatic detection, holding, and tracking of tar- gets is already feasible. Progress in this direction, however, for any but the most simple of sonar situations is likely to be difficult and slow. One step toward more reliable detection and classification is the improvement of the amplitude ratio of genuine signals to random signals by display integration methods, and we have given much attention to this. The effect of shape and size of the target display on the ability of an operator to detect and recognize it is another very relevant matter which has been under investigation. Classification by knowledge of frequency response of targets (c above) is very problematical at present, but we are trying to develop a wide-band system, having a 10 to 1 frequency band and constant directivity over this width, which can display this information and which will enable us to assess the potentialities of the method. Propagation of underwater acoustic signals is obviously a fundamental matter requiring continuous research in order that system improvements may be co- ordinated and exploited. Long-range propagation studies are beyond our facilities, but we have some interesting results on short-range echo formation which point to other limitations on the use of improved systems. 2.2, ARRAYS AND DIRECTIONALITY Throughout this section, directionality will be considered in terms ofa line or strip array, so that only two-dimensional directional patterns are involved. 2.2.1. Multiplicative Arrays In the search for higher directionality for a given size of array, the replace- ment of addition by multiplication in the combining of signals from different sections of the receiving array has some very definite attractions [1,2]. For instance, if a strip array is divided intotwo equal sections, and the output signals from these (assumed of narrow bandwidth) are multiplied together, the output of the multiplier comprises two parts (as far as the wanted signals are con- cerned), one a dc signal and the other a signal at twice the original frequency. The amplitudes of both these parts are functions of the direction from which the signal was received, although the double-frequency part is less sensitive to direction than the dc part. The directional response of the dc signal, plotted as the variation of amplitude as the array is rotated in the plane of its length, has a main lobe, or beam, which is only half the width of the main beam of the same array when used in the normal manner, i.e., with the signals from its sections merely added together. It is therefore attractive to regard multiplication (with a low-pass filter to remove the high-frequency output) as a way of doubling the directivity of the array. There are other advantages, too. In the ordinary (addi- tive) system, the output of the array is at signal frequency, and it is necessary D. G. Tucker 3] Fig. 2.1. Multiplicative and additive directional patterns for the same array of eight elements; (a) multi- plicative (b) additive. (b) to rectify this for display. Thus all the lobes in the directional pattern become of the same polarity (say positive). But in the multiplicative array, the output is de and the largest secondary lobes of the directional pattern are of negative polarity as is shown in Fig. 2.1. Thus, response from signals arriving from directions corresponding to these lobes can be eliminated by the use of a rec- tifier following the multiplier and its low-pass filter; or with an intensity-modu- lated display ona cathode-ray tube, signals from these directions will not brighten the screen. There are, of course, complications and disadvantages. One complication is that the doubled directionality strictly applies only to the directional variation of output from a single source as the array is rotated; it is not the same thing as directional discrimination. Whereas in the linear additive system direc- tional response and directional discrimination are essentially the same thing, in the multiplicative (and nonlinear) system they are not. Welsby has shown, how- ever, at least for some important practical situations, that resolution of two targets at the same range is approximately doubled [3]. The limited experi- mental experience we have so far had of within-pulse scanning sonar using the multiplicative system (see below, Section 2.3) adequately confirms this. The reduced secondary response of the multiplicative system has also been shown to be genuinely realized in a multitarget situation. One of the disadvantages referred to is the fact that signal-noise discrimination is 3 db worse than in the additive system. Welsby has recently discovered that some use can be made of the double- frequency output of the multiplier when the signals are of coherent type [4]. If this output is rectified and added tothe dc discussed above, then the signal-noise discrimination at the peak of directional response can be partially restored—to the extent of 1.6 db; and if subtracted instead of added, it can lead to a further narrowing of the main beam. The use of multiplicative reception has been known for a long time in con- 32 Lecture 2 nection with wide-band signals of continuous spectrum (i.e., noise emissions); in this case its use is natural since it provides the process of cross-correlation which is used so extensively in the mathematical consideration of such signals. But the use of the process in narrow-band (and coherent) echo ranging seems to be a new development and we are not aware that anyone else has been inves - tigating its practical problems. 2.2.2. Superdirective Arrays There is copious literature on superdirective arrays [5], to which we have contributed [6], but practical results are not conspicuous. There is no doubt that the academic interest of superdirectivity rather exceeds its practical utility. Naturally, the idea of obtaining a greatly narrowed beamwidth is very attractive, but there are numerous disadvantages and difficulties in this method of attaining the desired result: a. The signals must be restricted to a very narrow band. b. The sensitivities (or excitations, since the method is applicable also to radiators) of the various elements of the array must be set to extremely close limits. c. On reception, the signal-noise performance (in relationto receiver noise) is very poor; on transmission, the efficiency is very low. d. The calculation of a practical array is made very difficult—at present, perhaps impracticable in most cases—by interelement coupling, which is inevitably a major effect in an array where adjacent elements must be less than halfa wavelength apart and must usually operate in antiphase. It thus seems unlikely that there will be much serious development of super- directive arrays of the normally considered single-frequency multielement type. But it will be shown in the next section that multifrequency two-element arrays may encourage trials of superdirectivity for limited applications, since they almost eliminate the difficulty of interelement coupling. It seems fairly certain that multiplicative arrays are superior in most re- spects to superdirective arrays, since they are quite easily realized and give a much better signal-noise performance. Figure 2.2 shows how a particular directional improvement can be obtained in both ways, but while the multiplicative method costs only 3 db in worsening of the noise factor, the superdirective method costs 20 db. 2.2.3, Multifrequency Two-Element Arrays The idea of "space-frequency equivalence," where the effect of a multielement array is obtained from two elements used simultaneously at a number of fre- quencies, appears to be very recent [7,8]. The basic reasoning is simple; the | spacing of the two elements is a different number of wavelengths at each fre- quency, so that the use of a harmonic series of frequencies can give the effect of a uniformly spaced multielement array. Althoughthis kind of array is in some respects analogous to an ordinary multielement array, it has been shown that it is certainly not properly analogous [9]. Even to make equivalent transmitting and receiving arrays separately stretches the analogy somewhat, and it fails completely when one tries to associate a multifrequency two-element transmitter D. G. Tucker 33 RESPONSE t TO PEAK OF 7:5 1 AT X =277 PLAIN LINEAR ARRAY SUPERDIRECTIVE o:5 ARRAY (e) >=+—=—_—* 7° 30 7 2 ; Oe Arse MULTIPLICATIVE a ARRAY OPS = Fig. 2.2, Comparison of (a) normal additive, (b) multiplicative, and (c) superdirective directional responses for the same array. with a similar receiver; they just cannot work together. There is not space to deal with this question here (a full account is being published elsewhere [9]), and we must accept multifrequency two-element receivers as a special kind of array to be studied separately. Nevertheless, with care, some of the methods of ordinary arrays, e.g., the synthesis of superdirective directional responses, can be applied. The practical form of this kind of receiving array is based on the multipli- cative system, in which the outputs of thetwo multifrequency receiving elements are multiplied together, as shown in Fig. 2.3. The multifrequency signal sent from the transmitter comprises a group of r harmonics. On reception at the two elements, these harmonics contain directional information in the form of the phase angles +md, where ¢=(md/\) sin 0, dis the spacing between the ele- ments, and A is the wavelength at the fundamental angular frequency p. On mul- tiplication (and ignoring the "special filter" for the moment), the de output becomes a function of signal direction, thus vy, ye E2 cos 2m¢ m=1 If only odd values of m are used, and all E,, (for m odd) are equal, this becomes Y, E* sin(r + 1) Co) sing which is the well-known form of directional response for a linear array of uni- form sensitivity, with r+1 elements (which is an even number), except for a factor of 2 in the angular scale. 34 Lecture 2 5 SIGNAL = > Am cos (mpt +&m) m=1,2,3,.. ARRAY a » Em cos(mpt +x. +m) r i) » Em cos(mpt +%, - mg) : CUT OFF SPECIAL >rp FILTER MULTIPLIER r - DIC RES cos 2m¢ m=1,2,3,.. Fig. 2.3. Multifrequency multiplicative pair (with provision for superdirectivity). Now the amplitude £2 determines the "taper" of the array, and it is clear that, if desired, this taper (although effective at the receiver) may be imposed at the transmitter by giving different amplitudes to the transmitted signal com- ponents. But it should also be noted that if the transmission properties of the medium (or the target strengths in an echo-ranging system) are different at different frequencies, then an unwanted taper function will be imposed. When all harmonics are used (i.e., m=1,2,3,...), then, in the space-fre- quency equivalence, this corresponds toa multielement array with an odd number of elements but with the central element omitted. The effect of the central ele- ment can be obtained by adding tothe output of the multiplier a dc voltage derived from the square-law rectification of the output of one of the array elements. Superdirectivity can be obtained with this system; and if approached from the point of view that a particular number of frequencies (or pairs of elements in the corresponding "spatial," or multielement, array) is specified and that a superdirective response is to be obtained from it, then superdirectivity can be obtained easily. On this basis the problem reduces to (a) choosing p and d so that the number of wavelengths in d progresses by less than one wavelength for D. G. Tucker 35 PHASE - SHIFT ) 2p 3p 4p Sp 6p FREQUENCY Fig, 2.4. Phase—frequency requirement of special filter in Fig. 2.3. each step in m, i.e., the equivalent spatial elements are less than half a wave- length apart and (b) reversing the polarity of alternate frequency components. The latter can be done by inserting the special filter in one channel, as shown in Fig. 2.3, having a phase shift-frequency characteristic as shown in Fig. 2.4. The values of E,, are then chosen to give the required directional response. For more complicated cases of superdirectivity, it is always possible to separate the various frequency components before multiplication, multiply them separately, and then adjust amplitudes and polarity as requiredin the separate outputs before they are finally added together. It is clear that superdirectivity obtained witha multifrequency array removes much of the difficulty of interelement coupling that was mentioned in Section 2.2.2, since it is probably only at the lowest frequency that the elements are less than half a wavelength apart. The system so far described involves frequencies spread over a rather wide band; it may be useful at low frequencies where a full array would be too large for handling, but where a two-element array could have its transducers mounted, for example, on two different ships or ontwo different towed bodies. For narrow- band use at higher frequencies, the series of harmonics may be replaced by a series of frequencies (f + S8f) = nS S)Sir where 6 is small compared with unity. The frequency f should be transmitted at a relatively high level or be suitably enhanced or reinserted at the receiver [10]. The complex signals from the two transducers are separately envelope- detected before being multiplied together—see the example in Section 2.3.2. 2.2.4. Wide-Band Arrays Normally, echo-ranging systems have fractional bandwidths, although it is well known that detection is improved as the bandwidth is widened—and properly utilized. We are developing a really wide-band system—9 to 1 ratio of upper to lower frequency—so that frequency response of the target as well as its range and bearing may be displayed. One of the more important problems to be solved 6 Lecture 2 is that of obtaining a directional receiving transducer with its beamwidth con- stant over this wide frequency range. It will probably be satisfactory for the transmitter to be omnidirectional, and forthe systemto rely only on the receiver for directionality; however, the method to be described can apply to a trans- mitter if necessary. Since target bearing is to be determined, directionality in the system is clearly essential; but it must obviously also be constant at all the frequencies concerned, since it is hardly possible to correct for the angular position of the target in the beam. There are several ways of achieving a constant beamwidth. The Birmingham method [11,12] is to have an array divided into sections, which are connected, via decoupling circuits, into a number of phase-shifting networks (or delay lines) as shown in Fig. 2.5. These have a phase shift which increases with frequency, so that at each end the effective directional pattern is deflected by an amount which increases with frequency. Successive delay lines have a successively larger range of phase shift. Then, after correcting the phase of the outputs from the various lines so that they are all in phase at all frequencies, the outputs are added together. Now, at the lowest frequency ofthe range, the phase shifts in the lines are small (ideally zero) and the directional patterns all very nearly coin- cident; their addition therefore produces only the ordinary (sin x)/x pattern, corresponding to the number of wavelengths in the length of the array at that frequency. As the frequency is increased, the individual patterns begin to sepa- rate, so that their addition leads to a wider beam in terms of wavelength, but it DECOUPLING IMPEDANCES TRANSDUCER IN 19 SECTIONS AND SIMILAR CONNEC TIONS >> FOR ALL SECTIONS OF TRANS— — — DUCER AND DELAY LINES de) | ff i oe Aad Pod oa tea Eth co | a eal [a a | pm [es em ae | ADDING UNIT WITH PHASE CORREC TORS OU T PUT Fig. 2.5. Wide-band constant-beamwidth array: block schematic for frequency band of 9 to 1. D. G. Tucker 37 is arranged that the beamwidth in terms of physical angles remains very nearly constant; about + 10% variation over a9to1 frequency ratio was achieved. Figure 2.6 shows the state of affairs at the maximum frequency. Above this frequency, dips occur and the pattern begins to break up. An experimental array covering the frequency range 9 to 81 kcps has been built and tested in water. The theoretical results have been matched very closely. It is, of course, difficult to operate the transducers at good sensitivity over this wide frequency range, but wearetryingto develop a satisfactory capacitance transducer. 2.3. SONAR SYSTEMS 2.3.1. Within-Pulse Scanning Systems Using Multielement Arrays The idea of electronic sector-scanning sonar systems in which the receiving beam is repeatedly swung across the search sector, insonified by a wide-beam transmitter, at least once during each period of time equal to the duration of the transmitted pulse, is by now probably quite familiar. By this method, a virtually simultaneous examination is made in all directions withinthe search sector. For a sector equal to n times the 3-db beamwidth of the receiving array, the array has to be divided into n sections. Alternative arrangements for swinging the beam have been published; the system developed at Birmingham [13,14] uses phase-shift networks to link the sections of the receiving arrays, with frequency changers interposed in the leads from each array section. The local oscillation supplied to the frequency changers is swept through a range of frequencies with a repetition rate equal to the desired scanning rate; and since the phase-shift networks have a phase shift varying with frequency, the beam direction is swept over a sector in sympathy with the sweep of frequency. —— COMPONENT PATTERN o-8L sss RESULTANT PATTERN RELATIVE RESPONSE ait Fig. 2.6. Wide-band constant-beamwidth array: component and resultant directional patterns at upper frequency limit. 38 Lecture 2 Bearing a6" o 8 6+6 1 1 — ~~ Qu. u a Fig. 2.7. Scanning echo-sounder display with fish passing through sector. (Southern North Sea, depth about 20 fathoms; maximum range on scale, 25 fathoms.) (Courtesy, ——— Institute of Navigation, London.) 25 fathoms This method of scanning has been very successful, and the experimental equipment has been useful in examining fish shoals in connection with a fisheries research program of the Fisheries Laboratory at Lowestoft (see Fig. 2.7). The equipment has also been effectively demonstrated [15] as an aid to hydrographic and oceanographic surveying, both with horizontal beam (Fig. 2.8) and with ver- tical beam (Fig. 2.9); in the latter application it shows a complete bottom profile on a single pulse transmission, and this proves useful in bad weather when "quenching," by suppressing nearly all the transmissions, makes ordinary echo sounders useless. In these experiments, the beam was about 1.5° wide between 3-db points in the plane of scanning, and 12° at right angles to this plane. The frequency was 37 kcps, and of 1-msec pulse duration. The analysis and experimental investigation of the factors which limit the performance of this type of scanning system have been taken a long way [16], partly with the help of an electromagnetic analog [17] (i.e., a radar version of it), and currently a high-resolution system is nearing completion which exploits the system fully. This has 35 sections to the array, and with an operating fre- quency of 400 kcps will give a resolution of ie in bearing, 6 in. in range, over a 17° sector, with a maximum range approaching 100 yards; it is intended, among other things, to allow observation of the movements of individual small fish in a reservoir. The most striking achievement in this development at Birmingham is the successful application of the multiplicative principle to the scanning system [3]. Figure 2.10 shows in block form how it is done. This has resulted in a genuine doubling of the angular resolution for a given length of array, as illustrated in Fig. 2.11. In the experimental trial, of which this is one of the records obtained, D. G. Tucker ~ RIDGE ON SEA BOTTOM 800 yds ~ Fig. 2.8. Scanning sonar display with horizontal beam, showing ridge on sea bottom, (Shallow coastal waters, Southern England.) Gs us ae 10 fm. 4 7 7 7 Fig. 2.9. Scanning echo-sounder display, showing bottom slope of approximately 45° on Continental slope, Eastern Atlantic. (Courtesy, Institute of Navigation, London.) 7° 240 fm. 4 39 40 Lecture 2 N/a SECTIONS N/> SECTIONS TRANSDUCER INT SECTIONS SWEPT PHASE SHIFTER WITH | LINEAR PHASE - SHIF T/ AMPLIFIERS FREQUENCY RESPONSE IF NEEDED LOW -PASS FILTER TO DISPLAY Fig. 2.10. Block schematic diagram of scanning sonar system with multiplicative operation. two 18-in.-diameter air-filled steel spheres were suspended in the water, and one was carefully moved relative to the other. When on exactly the same range, they were moved together slowly while photographs of the B-scan display were taken, This was done for both ordinary additive and for multiplicative operation. The figure shows the sphere echoes just clearly resolved in each case, and it is quite obvious that the multiplicative system not only has half the beamwidth, but twice the angular resolution as well. The effect of the reduced secondary re- sponses of the multiplicative system is also shown clearly in Fig. 2.11, where the receiving gain was greatly increased. With the additive system, the beam and its secondaries have spread right across the screen, due to the high intensity of the signal relative to the display threshold, but with the multiplicative system an interpretable display is still obtained. 2.3.2. Within-Pulse Scanning Systems Using Multifrequency Arrays In the search for both better and cheaper scanning sonar systems, it is clear that the multifrequency two-element array (discussed in Section 2.2:3) has a potential attraction since it permits beam scanning to be done with a single variable time delay in one channel, in place of the complex series of phase shifters needed for the multielement array. Various kinds of variable time- delay networks are under consideration, but one which Welsby [10] has proposed for the narrow-band multifrequency system (mentioned at the end of Section 2.2.3) is of particular interest. His system is shown in block form in Fig. 2.12, D. G. Tucker 4] RANGE —+6° oO = 0g Ww [-2) =u 0 YARDS 30YARDS ie 20! (b) (d) (e) (fF) Fig, 2.11. Comparison of multiplicative and additive scanning sonars using same array (eight channels from array). (Courtesy, British Institution of Radio Engineers.) (a,b) Single 18-in.-diameter sphere at 30 yd: (a) additive system (b) multiplicative system. (c,d) Same as (a,b), but with receiver gain greatly increased to show effect of side lobes: (c) additive system (d) multiplicative system. (e,f) Two 18-in,- diameter spheres at same range of 30 yd: (e) additive system (f) multiplicative system. for the case where the frequencies transmitted consist of the center frequency @, and the two odd-harmonic difference pairs, w) +@,; and wo +3w;, where w; Kp. The output of one of the receiving transducers is translated in frequency to o,, @, +@;, and, +3, by means of a frequency changer fed with a frequency-swept local oscillation; thus w, is being swept through a range of frequency during every interval of time equal to the durationof the transmitted pulse. The narrow group of frequencies o,, o, +@;, andw,+3w, isthus swept up and down the delay — frequency characteristic (Fig. 2.13) of the "quadratic phase network" and re- ceives a different delay at different instants inthe sweep. The sonar information, being carried by the envelope amplitude of the complex signal, is then recovered by normal detection before being multiplied by the signal from the other trans - 7p) Lecture 2 Wo +3u, Wo +, Wo TRANSMIT Wo -W wy a | QUADRATIC | PHASE ' NETWORK Wet 3W TECTOR RECEIVE s 1 OETECTO 2 ELEMENT MULTIPLIER ARRAY TO DISPLAY Fig, 2.12. Multifrequency sector-scanning system. ducer channel. Since, in the channel from the other transducer, only a fixed delay is provided, it is clear that effective scanning of the beam has been obtained. The design of the delay network is based on the phase-frequency charac- teristic $=aw*+bot+c which can be obtained with reasonable accuracy bya low-pass filter section with an abnormally high value ( ~ 3) of the derivation parameter m. 2.3.3. Double- Transducer FM System As a result of his studies of echo location by bats, Kay has proposed a sonar system which, in addition to giving a possible explanation of the bat's echo- location acuity, indicates a line of development for man-made sonars which may be very profitable [18,19]. Suppose that the sector of search is insonified by a frequency-swept (or FM) continuous (or quasi-continuous) tone, and that two spaced transducers are used as receivers. If each of the latter is connected to its own conventional FM sonar receiver, then at the output of each receiver the range of any particular target is indicated by the frequency of the output echo signal. But if the target lies in a direction making an angle to the normal axis of the two transducers, the output frequencies will be different in the two receivers, since the ranges are different. D. G. Tucker 43 oO \ 2 3 4 oY) X= We Fig. 2.13. Graph showing the shape of the delay/frequency characteristics for an m-derived low-pass filter section with m= 3. The curve is a reasonable approximation to a straight line over the range x= 0.1 to 0.4. A filter section with m> 1 can be realized by the use of mutual inductance as shown, If then the difference frequency is obtained, this will be a measure of target bearing. (The sum frequency will be ameasure of mean range.) Thus, two trans- ducers will give a full sector search with no secondary-lobe effect, although in the simplest case there will be a left-right ambiguity. Even this latter can be removed by using a polyphase circuit for obtaining the difference frequency. The block schematic of the system is shown in Fig. 2.14. Kay suggests that this is the way bats obtain accurate obstacle- and prey-location with only two small ears. 2.4. DISPLAYS The theoretical investigation of displays has always been bedeviled by the difficulty of finding a criterion of performance which is both realistic and suit- able for mathematical analysis. Experimental work has been hindered by the subjective nature of the measures of performance. Thus, progress has been slow, as far as any fundamental improvement in detection thresholds is con- cerned. One contribution from Birmingham is the improved integrator described below. It is also thought that the work on pattern recognition to be described 44 Lecture 2 SCANNING SWITC R. RECEIVER switcH TO DISPLAY (RANGE ) SCANNING SWITCH. TO DISPLAY (BEARING) Fig. 2.14. Double FM sonar system. may eventually improve the use of visual displays. Of course, great progress has been made in what may be called the mechanics of displays, e.g., the writing of strobes, markers, and numbers in between signal scans, but we have not been concerned with this. 2.4.1. Integration and Correlation Sonar systems are only too often concerned with threshold detection, and it is therefore important to make the maximum use of information which may be repeated in successive range or bearing scans. The improvement of detection obtained with a paper (chemical) recorder when a target appears on several successive range scans, and thus appears as a line on the record, is well known [20]. The improvement of threshold signal—noise level has been shown to be about 2.4 db per doubling ofthe number of scans. The same method can be applied in cathode-ray displays of similar type, but it is, of course, not suitable for P.P.I. or sector-scan displays. For these latter, some improvement of threshold arises from either integration of successive signals on the phosphor itself, or from a human memory effect when successive pictures are mentally superposed. A more satisfactory basis of improvement, however, is properly designed in- strumental integration. Integrators using a delay line (e.g., mercury) as the storage element are well known, and used occasionally. Cooper and Griffiths [21] have not only estab- lished a basis for optimum design, but have also developed an improved inte- grator using two loopcircuits,as shownin Fig. 2.15. Working on the assumption of a P.P.I. display obtained from a single-beam echo-ranging system, with the beam rotated at a relatively slow rate (giving several echoes from any particular target on each sweep), and assuming a directional pattern of Gaussian shape, they have determined the proper loop gain for single- and double-loop integrators. These factors lead to the following optimum performance figures; all are ex- pressed as decibels-improvement in video signal-noise ratio relative to that of D. G. Tucker 45 DELAY LINE FEEDBACK NETWORK O OUTPUT INPUT DELAY LINE FEEDBACK NETWORK Fig. 2.15. Double-loop signal integrator system. a hypothetical (ideal) system in which the best weighting is given to every com- ponent signal at all times. a. Uniform weighting of the optimum number of signal returns, the system input being cut off before and after these returns—0.5 db worse than the ideal system b. Single-loop continuous integrator with optimum loop gain—0.95 db worse than the ideal system c. The new double-loop integrator with optimum loop gains—0.3 db worse than the ideal system In view of the fact that the double-loop integrator is thoroughly practical, its performance is so close to the ideal that its use seems well justified. It is somewhat surprising, however, that the investigation shows the form of the integrator to be so uncritical. What we do not know at present is how far the performance of ordinary P.P.I. displays (where there is some integration on the phosphor) falls below the performance of these properly designed integration systems. 2.4.2, Pattern Recognition and Size of Target It has been mentioned previously that the detectability of a signal in noise is improved by causing the signal to trace out a line on successive returns, as in the chemical recorder. It would be expected that, correspondingly, a signal pat - tern of any shape would show increasing detectability as its area increased re- lative to the "grain" of the noise background. Probably, the shape itself would have some influence on detectability. Recent experimental work by Nagaraja [22] at Birmingham, using a cathode- ray display, has shown that: a. Circular patches show a decrease in threshold of detection of about 2.3 db per doubling of area, provided the area is fairly small (<100 min? as 46 Lecture 2 -18 Oo ' yo sb 10 LOG (CONTRAST THRESHOLD) 10 100 1000 AREA IN SQ. MINS. Fig. 2.16. Area/contrast threshold relationship at background luminance of 0,1 ft-L. (A) Blackwell's data (B) With noise background—circular patch (C) With noise-free background—circular patch (D) With noise-free background—line patch. seen by the eye); this is the same rate as for a line (or slit) target patch. With larger areas, the rate falls off. b. With fairly low background luminance (0.1 ft-L), the threshold is almost the same whether the background is noise or merely a uniform bright - ness, but at higher background luminance (say, 1 ft-L) the threshold is much poorer for noise than for uniform brightness. This is consistent with the conception of internal noise in the human optical system. Figure 2.16 shows the results for a background of 0.1 ft-L, and also shows that these results agree well with those obtained with different experimental methods by Blackwell [23]. 2.5. ECHO-FORMATION AND RANDOMIZATION One of the most serious difficulties in sonar development is that, however good the array and system generally, there is always a limitation on performance imposed by the medium through which the system operates. In the medium, the sea, there are variations in temperature, salinity, aeration, etc., as well as currents, turbulence, and inhomogeneities generally, which affect to a greater or lesser extent the transmission of signals. There are reflections and scatter- ing at the bottom and surface of the sea which produce multipath transmission as well as an interfering background. The environmental conditions which have an adverse effect on sonar performance include the instability of transducer position when the equipment is shipborne. These various factors are very hard D. G. Tucker 47 SPHERE BOTTOM ECHOES ECHOES Fig. 2.17. Echoes from sphere and sea bottom on different trans- missions. Duration of first and second pulses in each transmission =0.25 msec; separation=2.5 msec. to evaluate. It is doubtful if they have received anything like their proper share of research effort. An illustration of the sort of thing that may make higher resolution an em- barrassment, and automatic recognition of targets impracticable, is an effect which has been studied at Birmingham recently [24]. It is the rather startling influence of small transducer movements on the echo amplitude (and waveform) from complex targets. One particular result may be quoted to demonstrate this. A 50-kcps beam of about 12° by 14° was pointed vertically downwards from the ship Discovery II anchored in about 12 fathoms ofwater in a tideway. The trans - ducer was stabilized against roll, although the water was dead calm. An 18-in. - diameter sphere was suspended a few feet above the bottom. The sonar equip- ment emitted, on every cycle of repetition, two 0.25-msec pulses spaced a few milliseconds apart. Figure 2.17 shows the oscilloscope record of the returned signals for two different emissions. The echoes from the sphere (which is a simple single target) remained substantially constant throughout the test, but the echo from the bottom (which represents a complex target) was completely randomized in amplitude and waveform from one emission to another. Indeed, as can be seen from the records in Fig. 2.17 the lower amplitude return is partially randomized even between the two pulses whichare only 2.5 msec apart. The only possible explanation for this effect is horizontal movement of the ship due to yaw, but the magnitude of this movement cannot even approach the wave- length in 2.5 msec, although from one pair of pulses to another it could be several wavelengths. Laboratory tests confirm this explanation, as can be seen from the results of a tank test at 500 kcps with different kinds of bottom configuration, shown in Fig. 2.18. 48 Lecture 2 MEAN VALUE @) $500 .¢ 4 250 Ww & DISPLACEMENT OQ 20 40 60 80100 120 140'160 180 200 220 240MM 1O» 20x 30x 40x 50x 60x 7OXx 80> MV 1000 750 a » MEAN VALUE = AGO) HORIZONTAL r L LACE MENT O 20 40 60 80'1I00 120 140'I60 180 200 220240MM 1OAX 20x 30A 40x 50>» 60x 7OX% 80> MV 500 400 a > < 300 (©) & 200 100 HORIZONTAL MOTION DISPLACEMENT Oo 20 40 60 80 I100 120 140' 160 180 200 220240MM lOxX 20X 302A 40» 50X 60X 7OX 8OX Fig. 2.18. Amplitude fluctuations due to lateral motion of the transducers in tank test at 500 kcps. Pulse duration 0.1 msec. Amplitudes recorded at fixed time-point in returned pulse. (a) Tank bottom covered with plaster of paris. grain size Mi sey lt t ve a , A wh agian omp heen DM y fe he : ' 7) wth @sibo HY ent c wpb ied) ! ote ait i UA Hh Pa ; ee + MW) arene ad my, hey Oh Sc Jol ean (ho mae / jeote Sale Papel 1 / 1 " bq) «A i ; . t ety Mery rT wha Kl nuk q Ma ea 1 iN \ 4@ | tpdeh 4) ean ‘| iy ih M \ i} KA) Lay MA iT \\ a ann i ah il Ve fin), Ad : eantits hall ee NTT eyo iT Tura, 1 ii PL 9 uy Chee LECTURE 3 EXPLOSIVE SOURCES D.E. Weston Admiralty Research Laboratory Teddington, Middlesex England 3.1. INTRODUCTION This paper deals with transducers, though of a rather special sort. In this type of "transducer" there is a rapid and irreversible conversion of chemical energy into acoustic energy. I will not be much concerned with explosions as such, but will deal with explosions as acoustic sources — particularly underwater explosions. Only so-called point sources such as simple blocks of TNT will be described, and various special sources such as explosive gas mixtures will not be considered. A good deal of the ground covered will be familiar to many. This paper falls naturally into three parts. The first (section 3.2) gives some historical background. The second or main part (sections 3.3, 3.4, 3.5, and 3.6) concerns the characteristics of explosive sources, and draws heavily on two recent papers [9, 10] which give more detailed informationthan can be presented here. Reference [10] concerns underwater explosions, and [9] presents some more general ideas which are applied in particular to underground explosions. The approach here differs slightly from that in [9, 10]. The third part (sections 3.7 and 3.8) describes some of the uses of explosions in underwater acoustics re- search and touches upon interpretation of results. 3.2. BACKGROUND Underwater explosions have been used as acoustic or seismic sources in many connections, in geophysics, navigation, communications, etc. They were first used for underwater acoustics research about the turn of the century and received fresh impetus at the time of the First World War. In this early work the pressure levels very near the charges were investigated, but charges as acoustic sources were used mainly for timing. More work was started during the Second World War, and since then much as been done in many countries. It was at this time that acoustic levels were first measured and used for the quantitative estimation of transmission loss [4]. Why use explosions for this? Briefly, it is because they produce a nice loud bang with energy in a wide fre- quency range, as discussed further in section 3.8. 51 52 Lecture 3 At the Admiralty Research Laboratory the main use of explosion sources has been in the investigation of transmission loss. In order to deduce the abso- lute transmission loss from the signal level it is necessary to know the source level. One also needs to know the source differences between the charges of different sizes and types that may have to be used, together with the depth dependence of source level. Thus it became necessary to make a general study of explosion sources, including the measurement of absolute levels and differ- ences at various depths. It may be noted that the most important parameter is often the acoustic energy rather than the peak pressure, since the pulse energy should obey the same acoustic transmission laws as the intensity froma continuous wave source. The spectrum level of the acoustic energy which has flowed through a unit area is often quoted in db re 1 erg/cm*-cps. Actually, it is usually fp” dt (pis the pressure) which is measured, comparable to p* forthe C.W. source, and strictly speaking these quantities do not obey quite the same transmission law as energy or intensity (e.g., near a free surface). 3.3. GENERAL IDEAS ON SCALING LAWS AND SPECTRUM SLOPES There is surprisingly little in the literature oncharge spectrum levels or on scaling laws, and what there is contains many misleading statements. Thus, the second part of the paper starts off with some general ideas which are applicable to any type of disturbance in a three-dimensional medium, and it is not essential to consider the mechanisms involved. However, to be specific, think of an explo- sion with charge weight W, so that total energy is proportional to W. Volume is also proportional to W, sothatthe linear scaling factor for both distance and time is w’%. More precisely one has identical pressure-time curves when these are plotted against reduced time tw /3 and measured at corresponding values of reduced range rW 4s This explosion-similarity principle is semitheoretical but confirmed by experiment. The scaling law may be applied to explosion spectrum levels, e.g., for a change from 1 1b to 50 lbwhere w'4 =3.68. It is necessary to make the additional assumption of spherical spreading, which leads to some appreciable though calculable errors, especially at the shorter ranges. Fig. 3.1 shows that the whole spectrum is shifted back in frequency by w 73 (3.68 in the example), corresponding to the w’4 time scaling. It is also raised in level by w’S (or 23 db in the example); the factor W comes fromthe change in total energy and the factor w’8 from the change in the bandwidth of any given portion of the spectrum. Consider now how the spectrum level depends on W at a given frequency. This dependency is a function of the spectrum shape, so that in general there is no simple scaling law for a fixed frequency. There is a simple law only in a region of constant spectrum slope (assuming a logarithmic plot), the index being the sum of the above 44 for general-level change plus the product of ', (frequency change) times the index of the spectrum slope. Table 3.1 shows some of the important practical laws. To make use of the laws given in Table 3.1, it is necessary to know what spectrum slopes to expect, and Table 3.II illustrates some useful general rela- tions between pulse shape and spectrum slope, together with the predicted scal- D. E. Weston 53 | = ff FREQUENCY SHIFT W 3 (faes) (50 Ib) SPECTRUM LEVEL IN 4/3 LEVEL SHIFT W 2 (2348) dB LOG FREQUENCY Fig. 3.1. Spectrum scaling. ing laws. It is best to start with the delta function in example 4 which is well known as having a flat spectrum; the other pulses are derived from the one above by differentiation. At least the middle five of these examples have important applications to explosions. Example 5 is perhaps not very obvious but is actually the most generally occurring case. It is possibleto show from the wave equation that +o f pdt bade) falls off with range faster than p itself, and at long ranges may be taken as zero. It follows that at sufficiently low frequencies the f*-spectrum slope holds, as does the w? scaling law. These two laws are of great generality and, besides holding true for the radiated longitudinal elastic waves, will apply to both shear waves and electromagnetic waves. The arguments are developed in more detail in [9], together with the differing laws for two- and one-dimensional propagation. TABLE 3.1. Scaling Law at a Given Frequency as a Function of Spectrum Slope Frequency dependence Weight dependence of spectrum level of spectrum level P W? 70 wi —2 w23 54 Lecture 3 TABLE 3.1]. Pulse-Shape Relations Spectrum level proportional to Example Schematic shape of Lowest derivative number typical pressure pulse that is Zero at Frequency band 3.4, DESCRIPTION OF UNDERWATER EXPLOSIONS The characteristics of underwater explosions are well established. Cole [3] and Underwater Explosion Research [8] may be given as general references and Weston [10] as a reference for acoustic effects. Upon detonation, the explosive is converted to incandescent gas at a very high pressure, and a shock wave is radiated into the water. The gas bubble expands and due to water inertia over- shoots its equilibrium radius; at its maximum radius the radiated pressure is slightly negative. The bubble now contracts, and in fact undergoes a damped radial oscillation. At each bubble minimum a further positive-pressure pulse is radiated, though only the first two of these bubble pulses are of much signifi- cance. When the shock wave reaches the surface it is reflected as a tension wave, which may cause cavitation. For moderate shocks the surface shows corruga- tions, sometimes known as the black ring, and for stronger shocks a spray dome is formed. The precise mechanisms are still uncertain, but the critical depth for corrugations over a 1-lb TNT chargeis (ub fathoms, suggesting a water-breaking D. E. Weston 55 (a) (b) Fig. 3.2. Surface effects for 1-lb charges at 5 fathoms; (a) corrugations (b) plume. tension of about 300 lb/in? There is a separate and sometimes more impressive surface effect known as the plume, which occurs when the oscillating explosion gases reach the surface. Figure 3.2 illustrates the phenomena of corrugations and plume for a 1-lb charge at 5 fathoms, and indicates that for most shots used in transmission experiments the surface effects are not spectacular. Acoustically, an underwater explosion does not behave precisely like a fixed low-amplitude source, both because of the high pressure generated and because the explosion source may move while radiating. It is worth listing the differences. 56 Lecture 3 30 Theory for7 S| 501b Charges — = a 5F @ ae Measured SFG oF / octave a & ° differences = x Qa 2 4 6 8100 2 4 6 81000 2 4 6 810000 Frequency (c/s) Fig. 3.3. Differences from a 1-lb charge. 1. There is a Riemann broadening and sharpening of the shock pulse; the latter keeps the viscous losses at the shock front at a high level. 2. Reflection at the sea surface is imperfect due to Cavitation. 3. Some of the lost energy may be reradiated eventually; due, for example, to water droplets falling back into the sea. 4. At small glancing angles a strong shock wave suffers an irregular type of reflection at the sea surface, which may be compared or contrasted with Mach reflection. 5. Due to migration under gravity the bubble pulses may be radiated from a reduced depth. ; Most of these points are usually unimportant but it is necessary to watch them. D. E. Weston 57 3.5. MEASUREMENTS AND THEORY FOR UNDERWATER EXPLOSIONS Experimental results have been arrived at using octave filters followed by small analog computers, which compute {v7dt, where v is the input voltage. The results in Fig. 3.3 show some measured differences between charges, with an average accuracy of +1 db. They show that there is no simple law, that there is a real variation with depth, and that there is general agreement with the theory (to be described later). It may be noted that at high frequencies the 50-lb results are in the region of the w3 or 111/,-db law, and that at low frequencies the de- tonator results are approaching the W? or 54-db region. For close shots it is possible to estimate the transmission loss theoretically and deduce absolute source levels from the measured signals. Some results are shown in Table 3.II]; there is little depth dependence above 140 cps. The accuracy is a little worse than that for the differences. Results for other charge sizes may be obtained by adding in the measured differences, and it then becomes possible to test the w'4 and w% scaling laws for the whole spectrum by shifting these spectra as in Fig. 3.1. It may be noted that the similarity and scaling laws of section 3.3 should apply to the bubble pulses as well as to the shock, provided that the depth is constant and there are no appreciable secondary effects due to gravity, etc. The result is shown in Fig. 3.4, all points lying well on a single line. Some of the minor discrepancies can be explained, e.g., the low-frequency 50-lbvalues are low in level because bubble migration under gravity suppreses the bubble pulse. The spectral peak at the reciprocal of the bubble-pulse time is evident for the detonator results in both Fig. 3.3 (70 to 160 cps) and Fig. 3.4 (8 cps). The agreement with theory in Fig. 3.4 may be noted. So far it has been demonstrated that the scaling laws work, and now the more detailed theory for the spectrum will be presented. This comes from a Fourier analysis of the shot pressure-time curves given by Arons [1, 2]. The shock wave may be represented as a sharp rise in pressure Po, followed by an exponential decay with time constant ft). Either bubble pulse may be approximated by two similar back-to-back exponentials, with peak pressure P; and time constant ¢, for the first bubble. The pulse shapes and the resulting energy-spectrum equa - tions are shown in Table 3.IV (where pc is the characteristic impedance). The average total spectrum at high frequencies is obtained by incoherent addition of the shock and bubble contributions, as shown in Fig. 3.5. At low frequencies the shock and bubbles may be replaced by their impulse values I,,/,, and 1, occur- ring at time intervals T, and T; = T, + T, together with a steady negative pressure. The results are also shown in Table 3.IV and Fig. 3.5. TABLE 3.1I]. Free-Field Source Spectrum Levels for a 1-lb TNT Charge at 60 Fathoms Frequency in cps Energy flux density in db - 13.9 re 1 erg/cm’—cps at 100 yards ue Lecture 3 wn oo at 100 yards) iz Theory Experimental points (octave) | 8 501b o IIb x 0-002 Ib Energy Flux Spectrum Level (dB wrt. lerg cm” cycle 2 4 6 810 2 4 68100 2 4 6 81000 2 4 6 810000 2 Frequency (c/s) Fig. 3.4. Source levels for 7-fathom charges scaled to 1 lb. Note that there are regions in Fig. 3.5 with dependence on f?, f° and f~?. The high-frequency bubble pulse gives an f~* law, and just below the spectral peak at the reciprocal of the bubble-pulse frequency there is a region with a law close to f*. The latter arises because of the particular values of the impulses / and intervals T; the last illustrationin Table 3.IV is closer to example 6 of Table 3.II than to example 5. There is a sort of cancellation which in practice is both im- perfect and variable, so that the experimental levels in this region are higher than the simple theory (see Fig. 3.4) and also rather variable. TABLE 3.1V. Underwater-Explosion Pulse Shapes and Spectrum Equations Schematic shape Spectrum equation Description 2 2p Shock E)(f) = a pel 15 +47 f ) 8 Tsu Bubble Be (ee pe\4Ai +47 F Impulse E, w=) [tt + I, cos2 mT, + 1, cos27fT3 — Nsin2 7£T3\7 Cc +11 sin2 7fT; + [7 sin2 7fT3 — N(1 — cos anit)” where N=Io +1, +12/27T; D. E. Weston 59 e ie 23 20 a 2 : ‘ES Summation aS formula 5% 10 Energy Flux Spectrum Level (dB wert. | 2 4 6 810 2 4 6 8100 2 4 6 81000 2 4 6 810000 Frequency (C/s) Fig. 3.5. Theoretical source spectrum for 20-fathom, 1-lb charge. It may be mentioned that Weston [10] shows some measure of agreement between theory and experiment for depth dependence. This dependence is mainly due to the changing bubble-pulse frequency and is only important below, say, 140 cps for 1-lb charges where, however, it can be very large. The position has been reached where the acoustic spectra of underwater explosions are generally well understood, though many small points remain to be explained. It is still usually bettertouse experimental rather than theoretical figures for differences and for source levels. 3.6. COMPARISON WITH UNDERGROUND EXPLOSIONS It is interesting to compare explosions underwater and underground, though the latter are much less well understood. Their mechanisms have been broadly described as a spreading explosive pulse which causes shattering or plastic flow of the solid material out to a critical radius, beyond which there is normal elastic wave propagation. The most notable thing about the transmitted signal is that seismic amplitude is experimentally found to be directly proportional to charge weight (O'Brien [6], Weston [9]). This is of course the same as the low- frequency W? energy law of section 3.3, which applies because all the high- frequency energy is attenuated in passing through the ground. It should be noted that this law with low-frequency energy proportional to the square of the total energy can work only if the low-frequency energyis a small fraction of the total. Efficiency as a seismic source improves as the size of the charge increases. There are very few measurements on underground-source spectrum levels, though the work of McDonal et al. [5] provides experimental verification of the f?law. The source spectrum may, however, be calculated from the model as- sumed [9]; Fig. 3.6 shows a much-simplified comparison of the spectra in the two media. The total energy radiated does not change much whether the explo- Lecture 3 60 F$ AINANDSYS *paryijduits yonur ‘erpeur juazajyip ut suorso,dxa 10} emdads aaneyay °9"¢ “SI 39YuNOS av3Nn 13A31 WNdYLI3dS D. E. Weston 61 sion is underwater, underground, or even in the air. The shock duration is similar underwater and underground, so that both spectra show a turning point near the reciprocal F, of this shock duration, and a similar high-frequency spec- trum. However, the low-frequency spectra are quite different since the average underwater spectrum is flat down to about F,, the bubble-pulse frequency. This arises because the restoring force underwater isthe hydrostatic pressure, lead- ing to a negative pressure phase ofmuch greater duration than the shock. Under- ground, the restoring force is the rock rigidity, the positive and negative phases are of comparable length, and the f? spectrum law starts just below F,. These differences mean that the underwater explosion isa much better seismic source; a typical calculation suggests 10% efficiency underwater and 0.05% underground. There is experimental evidence for this underwater superiority. 3.7. USES IN RESEARCH A very important aspect which should be included in any account of under- water explosions is the use of these explosions in acoustic research. The uses are manifold, even excluding seismic investigations of the sea bed, so I will not attempt to give a full list. One use is to investigate transmission loss, including such things as reflectivity and fluctuation measurements. Another is to measure reverberation: volume reverberation including that from biological scatters, surface reverberation, bottom reverberation, and reflections from distant topo- graphic features. There are several other possible uses, many little explored. (Shots were fired in a wide range of conditions - four shots to measure trans- mission and three shots near the receiver to measure reverberation.) A little more will be said about the investigation of what may be considered the central problem in underwater acoustic research, i.e., transmission loss, Most investigators apparently use similar techniques, which are not particularly novel. Typically, one goes to sea with two ships. One ship is used for sound reception, with one or two hydrophones suspended in the sea. The second ship opens range while firing charges, possibly using a safety fuse. Alternatively, there may be serials at constant range, varying the depth of the charge or the hydrophone. Normally, the signal energy levels are measured using analog com- puters, but there are possibilities for other processing methods, such as the digital computer. For some purposes, peak pressures may be measured. Worth- while precautions include monitoring overload in all channels, scheduling some close shots as a check on source level and on the whole system, and measuring rather than estimating any differences between different charge types. In the typical trial, a large quantity of information is collected and a large analysis headache is generated. Lastly, note that one should beware of overload; in shot work this is of extreme importance and cannot be stressed too often. Figures 3.7 and 3.8 show two examples of results achievable with explosion sources, both taken with 1-lb charges in water of constant depth. Only a very little will be said about the physical meaning of these plots. Figure 3.7 shows a composite frequency plot for a range run in the Norwegian Sea, with 58-fathom source and 140-fathom receiver. Signal level itself has been plotted, and this is a first stage in presentation which is useful when source level may not be accurately known. Note that at low frequencies there is hardly any departure Lecture 3 +40, +30 | oF EO 4 =. —t ra +10 TOTAL see 5 O° d LJ He. | a. te | ERG/CM -1O- pe | aaa amos, -20 : sanih 35% aie aoe: 8) | 70% (-20dB) > -50 | See aeh — ros : j | ti -70 SS =e oT eA8 ap — 140% (40d8) - : | ete FR, 2p Pe -B0 Je oh Froeny a a -90) : 5-8-6, as) 1 tr a: DBO”S C60dB) x | | Ory wo 3 -| a : } | » “120 ital sso tee | | ae__ 560% (-B0dB caiea LSS. el if ee 5 Py &\ Wes fo) i | l 1 Ss = é S———— SS Saka __ ore Z 150) ie S Sa. Gooas) > -160} ) a = SK SS, He | a | x \ -17O}-— — 4 +] > A 7 -|180— = = F 4 200% Og Men N.— Cl20dB) 5 Wh, -200 ir — 65 i 3 -210) ine L 4500 % (-140 dB) -220} | | | és ia sill | 02 04 O06 08 10 2-0 40 60 8010 20 40 RANGE FROM HYDROPHONE IN NAUTICAL MILES Fig. 3.7. Sample contour transmission run in 666 fathoms. 63 *aBuer Satu ZT INoge pue yAdep JoleM SulOYyIey 0” - 0S- 7, LE ‘ssoy UOISSIUISUeD Jo aduapuadep dap jo aydwiexi] “g*¢ “BI SOUVA 00! WOU SP NI SSO1 NOISSINSNVYL WOLL08 | $/3 082 gk L =i RO aaa L f wee ne S/2 7-2 s/2 ¥ bb $/3 095 WOLL08 (J9NVY W6-SL) “QAH Hii £2 —¥- (JONVY W2-21) ‘QAH HVS 0€ —o— D. E. Weston $/3 O71 SWOH1V4 NI Hida0 JDYVHI 64 Lecture 3 from the cylindrical spreading law right out tothe extreme 40-mile range. How- ever, at the higher frequencies there is additional attenuation. Figure 3.8 illus- trates depth dependence in a North Sea area and shows the second stage of pre- sentation when transmission loss itself is plotted. This is an improvement, but it is recommended that in suchcases the assumed source level always be quoted. (Figure 3.8 assumed source levels and depth dependence based on Weston [10]; see also Table 3.III.) It may be seen that the transmission loss increases as either boundary is approached, because each boundary acts as a free surface. This is true for the bottom because the measurements were made in August when there is apparently a large quantity of gas held there. The details of the curve shapes may be explained as due to the addition of a number of modes. In August there is a strong thermocline at 15 fathoms. Thus the lowest modes are trapped below the thermocline and tend to produce a signal maximum at about 25 fathoms: some intermediate modes produce a maximum above the thermocline near 7 fathoms, and the higher modes show little depth dependence. It is possible to make the arguments for Figs. 3.7 and 3.8 quantitative, and learn about bottom character, etc. 3.8. RELATIVE ADVANTAGES OF UNDERWATER EXPLOSION SOURCES The competitor to the underwater explosion source isthe projector radiating continuous waves. Comparative measurements of transmission loss have been made at various times using projectors and explosives, and when done carefully they agree on average. However, a pure-tone continuous wave transmission will often show very large fluctuations due to interference effects, which are smoothed out when using the larger bandwidth in the charge experiment. Thus, to study average transmission loss one should use shots or a projector radiating band- limited noise; whereas to study fluctuations one would probably use a pure tone from a projector. In summary, most measurements may be made witheither source. There are many measurements that can only be made witha continuous wave source. There are a few measurements which virtually can only be made with explosions; for example, to study low-level arrivals one needs the very high pulse power of an explosion. In practice, experimental convenience plays a big part; a shot needs no auxiliary equipment and is almost unrestricted in depth. In passing, I wantto comment on Dr. Schofield's [7] remarks on the necessary sizes of projectors for reasonable efficiency, and to consider production of acoustic energy at 1000 cps. Here the electroacoustic device needs to be about 2 ft across, whereas a spherical charge of only about 2 in. in diameter (say, of lb TNT) converts about half its chemical energy into acoustic energy centered at 1000 cps. This high efficiency at low frequencies is only possible because of the finite amplitude effects near the source. I could have stretched my case further since the same 2-in. charge would have a bubble-pulse frequency of the order of 20 cps, but this would be cheating since the 20 cps is really associated with the maximum bubble diameter of a few feet. In conclusion, to be well equipped for research one needs to be able to use both continuous wave and explosion sources, depending on the experiment. Personally, I consider this likely to be the position for a long time to come. D. FE. Weston 65 3.9. ACKNOWLEDGMENTS Figures 3.3, 3.4 and 3.5 are reproduced fromthe Proceedings of the Physical Society published by the Institute of Physics and the Physical Society [10]; and Fig. 3.6, from the Geophysical Journal published by the Royal Astronomical Society [9]. REFERENCES 1. A.B. Arons, "Secondary Pressure Pulses Due to Gas-Globe Oscillations in Underwater Explosions: II. Selection of Adiabatic Parameters in the Theory of Oscillation,” J. Acoust. Soc. Am., Vol. 20, 277- 282 (1948). Be das }Bhs eee "Underwater Explosion Shock Wave Parameters at Large Distances from the Charge," J. Acoust. Soc. Am., Vol. 26, 343-346 (1954), 3. R.H. Cole, Underwater Explosions (Princeton Univ. Press, Princeton, New Jersey, 1948). 4. C. Herring, "Physics of Sound in the Sea, Part I, Transmission,” NDRC Summary Technical Report, Div. 6, Vol. 8 (1946). . F, J. McDonal, F. A. Angona, R.L. Mills, R. L. Sengbush, R. G. van Nostrand, and J.E. White, "Attenua- tion of Shear and Compressional Waves in Pierre Shale,” Geophysics, Vol. 23, 421-439 (1958). . P.N.S, O'Brien, "Seismic Energy from Explosions,” Geophysics, Vol. 3, 29-44 (1960). . D. Schofield, "Transducers,” Inst. on Underwater Acoustics (1961). . "Underwater Explosion Research," Office of Naval Research, Joint Anglo-American Compendium of Reports in three Volumes (1950). 9. D. E. Weston, "The Low-Frequency Scaling Laws and Source Levels for Underground Explosions and other Disturbances," Geophysics, Vol. 3, 191-202 (1960). 10. D.E. Weston, "Underwater Explosions as Acoustic Sources," Proc. Phys. Soc. (London), Vol. 76, 233- 249 (1960). CONTI O on DISCUSSION PROFESSOR M. FEDERICI asked whether the change of shape of the shock wave, as it progresses, had any influence on the scale law. MR. WESTON: The explosion-similarity principle takes account of the main changes in the shock-wave shape; but, to proceed from there to the w3 and Ww spectrum scaling laws for a fixed range, it is necessary to assume spherical spreading. In fact, the peak pressure falls off faster than this (with an extra factor of 1.13 in the index) and, at the same time, the shock-wave duration in- creases slowly. This necessitates some small corrections to the above laws, leading, for example, to a slight increase in the expected dependence of high- frequency spectrum level on charge weight. At stillhigher frequencies or at long range, there is, in addition, a falling-off in spectrum level due to a lengthening of the shock rise time. This last effect is not taken into account in the explosion- similarity principle, since the latter implicitly assumes an instantaneous rise. PROFESSOR T.S. KORN asked the order of velocity change in the shock wave as compared with the normal sound wave and whether the normal laws of dif- fraction were applicable. He also inquired if a slow-burning explosive material led to some improvement in the over-all efficiency as a source. MR. WESTON: Very near the charge, the shock velocity is a few times greater than the normal sound velocity; but, at distances of several charge radii, it is only fractionally greater. I think that some modifications to normal diffraction theory might be necessary. On the second point, the underwater acoustic outputs of slow-burning and high explosives are very different. The main wave from the former is of rounded form; compare the sharp rise of the 66 Lecture 3 high explosive shock. The total energy in the pulse from the slow-burning ex- plosive is much less than for the high explosive. Thus, the former may be re- garded as a low-efficiency acoustic source, whereas it is unlikely the efficiency value of about 50% for a high explosive could be much improved. The pulses from the two explosive types have a comparable impulse and, therefore, comparable low-frequency energy, but the rounded pulse produces negligible high-frequency energy. Also the gas bubble from the slow material does not greatly overshoot its equilibrium radius, so there is little bubble oscillation and very little energy in the bubble pulse. Since the bubble pulses contribute a good proportion of the low-frequency energy for high explosives, thenet resultis that the slow material is down over most of the spectrum (very low frequencies have not been investi- gated and could be an exception). LECTURE 4 THE IMPROVEMENT OF VIBRATION ISOLATION G.G. Parfitt Imperial College of Science and Technology London, England 4.1. INTRODUCTION The noise and vibration generated by a ship's engines and machinery will to a greater or lesser degree be transmitted to its hull plating by air-borne and, Particularly, structure-borne paths and be radiated into the surrounding sea, thus helping to disclose the ship's presence to passive listening devices. Ef- fective isolation of machinery vibration from its supporting structure may thus be of especial importance in naval applications. The present paper examines the elementary principles of vibration isolation and discusses various potential means of improving on the simplest form of spring isolator. This discussion is based mainly on work done at Imperial College and the University of Michigan by Dr. J.C. Snowdon. The simplest idealized resilient isolation system may be depicted as in Fig. 4.1a by a simple spring of stiffness (force-to-displacement ratio) S sup- porting a machine, represented by a simple mass M, above an infinitely rigid foundation. The mass is supposed free to move only in the vertical direction, under the action of an applied force F. A force F, is transmitted to the foundation, and the ratio F,/F is termed the transmissibility T of the system, or in decibels T = 20log (1) Here, 1/T or -T in decibels is a measure of the isolation. The system has a natural resonance frequency w 9/27 given by @6 -3 (2) If the spring stiffness S$ is linear and frequency-independent, the downward deflection d of the spring under the weight Mg of the supported body is given by Sd= Ms, whence -§ (3) 68 : Lecture 4 +40 F = 6 v0 Ww “N uw e = s a a o F a 7 u = -40 g c¢ 2-S/M = Wo = -80 0.1 10 100 (a) (b) Fig. 4.1. The idealized simple mounting system and its transmissibility curve. If the forces concerned are sinusoidal, with amplitudes F and F, and frequen- cy #/27, the transmissibility as a function of w is as given in Fig. 4.1b. No isolation is achieved unless o> ¥2o,. At high frequencies T varies as 1/o?, as in Eq. (8), i.e., decreases at 12 db per octave. It is therefore necessary that @ 9 fall below all significant frequency components present in the spectrum of the exciting force F. If it is not practicable to make the springs soft enough to achieve this—and Eq. (3) shows that irrespective of the nature of the spring, so long as it is linear and frequency-independent as stated, a low natural frequency necessarily requires a large static spring deflection—then w, must fall between and not close to any strong low-frequency spectrum components. The process of isolation is of course a purely reactive one, and no means of absorbing vibrational energy is necessarily involved. 4.2, ADDITIONAL CONSIDERATIONS The foregoing simple theoretical predictions are in general well borne out by measurements on mountings of a mechanically simple character [1]. Effects of finite damping, to be discussed below, of course modify the transmissibility G. G. Parfitt 69 curves, and an additional feature in practice is the presence at high frequencies of so-called "wave effects." These are the result of standing waves within the body of the resilient material and lead to some loss in isolation. They are not usually large in rubber mounts, but may be serious in, say, steel coil springs with very low damping. For this reason it is common to insert a rubber pad under a coil spring mount to give additional high-frequency isolation. In spite of the fact that it forms a very useful starting point for discussion, the system of Fig. 4.la is nevertheless a substantial oversimplification of a practical mounting system in several respects. First, practical mechanisms do not normally have only one degree of freedom, but many degrees. There will thus be many natural modes of oscillation, and hence many resonances; in gen- eral there will be coupling between them. These effects are likely to complicate rather than invalidate the discussion which follows, and they will be ignored henceforth. They are of course extensively dealt with in standard texts [2 to 5]. Secondly, the foundation on which the isolator rests will never be infinitely rigid, particularly in marine applications, and this will modify the transmissi- bility. In such cases of nonrigid foundations, it is often more instructive to use in place of T some other measure of isolation describing the extent to which the motion of the foundation is reduced by the isolator. One which has been used [6] is the so-called response ratio R, namely, R= : amplitude of foundation under isolator : (4) amplitude of foundation with M rigidly attached to it The same exciting force at the same frequency is assumed applied to M in each case. "Amplitude" here may refer to the displacement, velocity, or acceleration of the foundation, or even to the force upon it, for at a given frequency force will be proportional to motion. If the mechanical impedance of the foundation is at all frequencies very large compared with that seen looking into the base of the mount, then R is identical with Tas shown in Fig. 4.1b. If the foundation consists of a pure mass MM, or a pure spring of stiffmess S;, the resulting response-ratio curves are those shown in Figs. 4.2 and 4.3, respectively. The curve for the mass foundation is of the same form as Fig. 4.1b, but the resonance frequency is increased, leading to a reduction of isolation (increase in T) at high frequencies in the ratio M+M; 5 i (5) With an elastic foundation the resonance frequency is somewhat less than with a rigid foundation (negligibly sointhe case shown in Fig. 4.3), and the curve contains a trough due to removal ofthe original resonance of the main mass M on the elastic foundation [which gives a maximum for the denominator of Eq. (4)]. Above this frequency the response ratio reaches the constant. value S/(S + S;). Thus, in both these cases the response ratio, i.e., the gain from inserting a spring mount, is less at high frequencies than it would be with a rigid foundation. However, it is worth noting that this is not so much due to an impairment of the action of the mount, but to the fact that before the mount is inserted the in- ertia of the body to be supported is already relieving the foundation of part 70 Lecture 4 +40 {e) RESPONSE RATIO (db) -40 -80 0.1 | 10 100 1000 Fig. 4.2, Response ratio of a mount on a masslike foundation (schematic). of the applied force, i.e., some isolation is already present. This effect vanishes as the foundation becomes increasingly rigid. In practice, foundations would have both spring- and masslike properties, with one or many internal resonances. Thus a foundation with one resonance gives a response-ratio curve (Fig. 4.4) which is essentially a combination of those of Figs. 4.2 and 4.3, but it has a new peak corresponding to the foundation resonance. Above this the curve shows a shift to the right compared with that for a rigid foundation, as in Fig. 4.2, and the loss in isolation is again (M + M)/M;. With a multiresonant foundation such as a metal beam, the response ratio is as in Fig. 4.5, showing now a progressive shift to the right. A word of warning about the interpretation of such curves may be in order. In general, apart from the basic mounting resonance, they will show pairs of adjacent troughs and peaks, representing the positions of the foundation reso- nance before and after inserting a mount. Thus the existence of such a peak, i.e., a region of poor isolation, is not necessarily an indictment of the mount's Performance, but simply indicates that a shift of a resonant frequency has oc- curred which may or may not be deleterious depending on whether the peak moves closer to or further from any strong components in the excitation spec- G. G. Parfitt +40 RESPONSE RATIO (db) b fe) 0.1 ! 10 100 1000 Fig. 4.3. Response ratio of a mount on an elastic foundation (schematic), +40 {eo} RESPONSE RATIO (db) b {e) 0. | 10 100 1000 Fig. 4.4. Response ratio of a mount on a resonant foundation (schematic), 71 72 Lecture 4 +40 -40 RESPONSE RATIO (db) 0.1 | 10 100 1000 Fig. 4.5. Response ratio of a mount on foundation with multiple resonances (schematic). trum. A more generally significant feature of the response-ratio curves is the presence of any upward or downward shift of general level. A third way in which Fig. 4.1a is anoversimplification is in that the mounted item will not in general behave as a pure mass except at low frequencies. This effect has not been widely studied in the literature, but might be expected to produce effects qualitatively rather similar to those of nonrigid foundations. Three main directions are apparent in which the performance of a simple spring isolator of given static stiffness couldbe improved. The first is to reduce its resonance frequency with a given mass. This can only be done by making the dynamic stiffness decrease with increasing frequency or with increasing load. Unfortunately, in all real materials where stiffness varies with frequency, the change is in the undesired direction and so merely detrimental. Systems can, however, be devised which are nonlinear in such a way that the dynamic stiffness for small vibratory motion is well below the average stiffness con- trolling static or quasi-static deflection. One such system is a strut which is buckled under the load of the machine; another employs two conventional springs, one tending to pull the mass away from its equilibrium position due to the other [2]. One difficulty with such systems is that of making them effective for motion in more than one direction. G. G. Parfitt 73 A second improvement in a mount is to reduce the height of the basic reso- nance peak in its transmissibility curve by damping, or otherwise. One obvious reason for this is that, particularly inthe presence of random vibrational forces, it may not be entirely possible to avoid excitation at the resonance frequency. Other secondary reasons are the avoidance of temporary resonance during the run-up or stopping of a rotary machine, the minimization of oscillation following shock or other stray disturbance, and, as will be shown below, a possible damping of foundation resonances. A third beneficial step is to increase the rate at which isolation increases above the resonance, so as, for instance, to reduce the levels attained by the foundation resonance peaks of Fig. 4.5. Such ends can be achieved by damping or by adding mass to the system in various ways, and the resulting effects will be considered in what follows. 4.3. DAMPING OF SPRING ISOLATORS If the isolator spring is damped, its performance for sinusoidal forces can be represented by treating its stiffness as a complex quantity S*, viz., S* = S(1+ 7) where 6 is the damping coefficient. Both S$ and 6 may be functions of frequency in general. One important case, to which many fairly lightly damped solid ma- terials conform approximately, is that where S and 6 are constants. Another is the case of pure viscous damping, in which S is constant and 6 is proportional to frequency. Writing 5 GeHE& (6) ®o then defines the constant 5, the damping ratio, which is equal to the ratio of the actual damping present to that required to give critical damping of the sys- tem at its resonant frequency. Ghul The transmissibility 7 for a damped mount on a rigid foundation is given in general by T? nN 1+ 5? (1 — w?So/w2s)? + 8? (7) where § is the stiffness at frequency o and S, that at the resonance frequency @. This equation is plotted for 5= 0 in Fig. 4.1b. Introduction of heavy damping obviously will reduce the resonance peak, but in general will detract from the high-frequency isolation. Thus, with S = So equal to a constant and 5 constant, Eq. (7) reduces for w > wo, to 2 e 2% (0 8 Pash (E3) (8) or for S and Sconstant [Eq. (6)] to T= 25(=2) (9) 74 Lecture 4 +20 -40 TRANSMISSIBILITY (db) -80 0.1 0.3 1.0 =e w 3 10 30 100 ®o Fig. 4.6. Transmissibility curves of simple mounts with various types and degrees of damping. (a) 5=0.1, (b) 6=1.0, (c)6 =0.5, (d) modulus and damping as in Fig. 7c. Equation (8) represents only a relatively small loss of isolation compared with an undamped mount, but Eq. (9) gives a serious loss due to the large viscous stress set up at high rates of shear (or high frequencies). The full transmissi- bility curves are shown in Fig. 4.6, curves b and c. High damping of the order of 6= 1 can be obtained in high polymers, and though there it may not be greatly frequency-dependent, it tends to be accompanied by an elastic modulus which increases with frequency. In fact, it can be shown [7] that in a typical polymer having a wide spread of viscoelastic relaxation times there is an intrinsic relation between the two, viz., : za(logs) Thus, for example, 5=1 implies an increase of some 19 times in stiffness over a frequency range of two decades. The increasing stiffness leads to a loss in isolation (relative to that of an undamped mount) which in practice is similar to that caused by large viscous damping (curve cof Fig. 4.6). Thus, for example, if in Eq. (7) $/S9 = @/w» and 6 is constant, then for w > wo P= (1-467) (0) (11) which has the same frequency dependence as Eq. (9). In addition, polymers with high damping are rather prone to show substantial creep or "compression-set" effects under a static load. The frequency dependence of viscous damping, such as may be obtained from a simple dashpot device, may be mitigated by the use of a multiple isolator element containing two springs and a dashpot, as in Figs. 4.7a or 4.7b. These two forms are identical in performance and have an effective stiffness and a G. G. Parfitt 75 (a) DAMPING COEFFICIENT & MODULUS RATIO (b) RELATIVE FREQUENCY (c) Fig. 4.7. A damped spring system with a single relaxation time (a,b) and its modulus and damping spectra (c). damping factor both of which vary as in Fig. 4.7c. Stiffness still increases with frequency but does so now only over a limited range of frequencies. For a maxi- mum damping factor of unity the over-all increase of modulus between very low and very high frequencies is 5.8 fold. If such a system is arranged to have a maximum damping factor of magnitude unity placedat the resonance frequency of the mounting system, then the resulting transmissibility curve would be that given by curve d in Fig. 4.6. It isseento achieve a low resonant transmissibility with less sacrifice at high frequencies than the simple viscous damper or the high-damping polymer. The systems of Fig. 4.6 are compared on the basis of a common resonance frequency. A fairer basis of comparison would be that of a common static stiffness, as this determines the static stability of the equipment. In this case the relaxation curve d would be shifted to the right by a frequency factor of about 1.6. However, the curve for a high-damping polymer, at present indicated as coinciding approximately with the viscous-damping curve, would be shifted considerably more owing tothe larger ratio of high-frequency to static moduli. Snowdon [8] has studied the properties of a mount consisting of sections of a lightly damped natural rubber (hevea) and of a highly damped polymer placed mechanically in parallel. By suitable choice of material and relative cross section it can be arranged that the natural rubber provides most of the stiffness, which is therefore not strongly dependent on frequency and not too subject to static creep, while the other polymer contributes considerable damping. In this way a transmissibility curve combining substantial resonance damping with little loss in high-frequency performance can be obtained. Such a mount does not 76 Lecture 4 escape from the dilemma represented by Eq. (10), but represents a means of obtaining a good practical compromise between the conflicting requirements with available materials. Snowdon has also shown [8, 9, 10] that substantial damping in a mount at high frequencies is useful in suppressing any peaks occurring in this region due to foundation resonances (as in Fig. 4.5). This comes about since resonant vi- bration of the foundation with anantinode belowthe mount will involve substantial deformation in the mount, the mounted mass remaining almost stationary. Those mounts having high damping at high frequencies may therefore be useful here. A similar effect is of course achieved by adding damping material to the founda- tion structure [11], and may in particular be more effective for the higher-order modes of the foundation. Moderate damping of the foundation has relatively little effect except near the foundation resonance frequencies. 4.4. ADDITIONAL MASS IN VIBRATING STRUCTURES As might be expected, the transmission of vibration through a system may be reduced by making certain parts of it more massive, particularly in such a way as to introduce or emphasize differences in mechanical impedance between adjoining parts of a structure. Taking the idealized case of a mass m supported by an isolation spring at the center of a beam (Fig. 4.8), an additional mass can usefully be added either to mM itself, to the beam either distributed along its length or concentrated at the base of the spring, to the spring at some point along its length, or attached to M via an additional spring. These possibilities will be considered in turn. Increasing the mass of the mounted item merely reduces the resonance frequency 9 as M~“, with a corresponding gain in high-frequency isolation (for a rigid foundation) proportionaltoM. Alternatively, a stiffer spring, giving greater static stability, may be used for the same resonance frequency. The extra mass also serves to reduce the motion of the machine or equipment itself at high frequencies, and may be used to provide a more rigid base for the machine. The effect of adding a mass m to the base of the spring has been investigated by Snowdon [9, 10] from whose work Figs. 4.9 and 4.10 are taken. Figure 4,9 shows the response ratio for a system in which the mass ™, of the supporting beam foundation is ha of the supported mass M, and in which masses m equaling 0, 0.1, 0.2, and 1.0 times M are attached at the beam center. The natural fre- Fig. 4.8. The idealized simple mount and resonant foundation. M¢ G. G. Parfitt 77 RESPONSE RATIO, R (db) | 5 10 50 100 500 1000 FREQUENCY (CPS) Fig. 4.9. Response ratio of the system of Fig. 4.8 with masses m added at the beam center. M = 50M;, 0;= 0.01 [10]. quency of M on the spring mount on a rigid foundation has been chosen as 5 cps, and the beam damping factor 6; as 0.01. Response ratio is here taken as the ratio of amplitudes or forces at the beam center after and before the spring 78 Lecture 4 RESPONSE RATIO, R (db) -100 FREQUENCY (CPS) Pig: an wees ratio of the system of Fig. 4.8 with masses m added at the beam center. M=10M,, fine 1 [10]. mount and the mass m are inserted together. Since the ratio of force applied to the end supports of the beam to the amplitude or force at its center is the same with or without the spring and mass present, the response ratio is also the ratio of support forces after and before the spring and mass are inserted. G. G. Parfitt 79 It may be seen that at high frequencies there is a large gain in the effec- tiveness of the isolation if a mass comparable with the supported mass is added to the beam. For the simple case of the single-resonance foundation used in Fig. 4.4 the response ratio at high frequencies is given by M+MA/oo\" nf) aa This equation also describes the high-frequency behavior in Fig. 4.9 tolerably well when mis appreciable. In particular it shows that when m=M, then R = (@/w)’, which is the value for an undamped mount on a rigid foundation. The process at work here is of course simply that in which the inertia of the mass m relieves the beam of much of the force transmitted through the mount. Another very apparent effect is that the effective foundation resonance is brought down in frequency by the mass m, in this case from some 70 cps to 8 cps for m=M. (More exactly, the mass largely nullifies one effect of the spring mount in detaching the mass M from the beam and allowing the foundation reso- nance to rise from its loaded value of5 cps to 70 cps.) This could be detrimental if there are strong excitation components in the low-frequency region, such as the rotor frequency of a machine. Figure 4.10, where the mass M is ten times the beam mass M;, and the beam damping factor has been increased to 0.1, shows the same general effects, but the frequency shifts are of course smaller and the resonant peaks due to beam resonance lower. It will be observed that the curves for m/M =1.0 show no indication of beam resonances other than the lowest, and in fact at higher frequencies agree closely with the transmissibility curve for a mount on a rigid foundation. This should not be taken to imply that the amplifying effects of the higher-order resonances have been eliminated from the system, but only that they are similar with and without the spring mount and mass inserted. Other results of Snowdon show that applying the same additional mass distributed along the foundation beam is less effective than adding a concentrated mass under the mount. The third possible position for additional mass in the system is at a point subdividing the isolator spring, typically into two equal sections. The isolator can then be regarded as atwo-stage unit and has been termed a compound mount- ing (Fig. 4.1la). Being a two-degree-of-freedom system, it has two natural resonances, and typical transmissibility curves will appearasin Fig. 4.12 [6,9]. These are calculated for a typical vulcanized rubber (hevea). As the ratio 6 of the secondary mass halfway down the spring to the main supported mass M in- creases, the secondary resonance frequency moves down towards the first. Above the secondary resonance, the isolation (for little or no damping) increases as o* instead of w? as for the simple mount (6 = 0). If strong damping is applied to the springs to suppress the resonances, some penalty is paid in high-frequency loss, just as for the simple mounting. It will be seen that unless the secondary mass is of a magnitude comparable with the main mass, any advantage of the compound system over the simple is not realized until a frequency is reached where the isolation of either is already very good. When used on a nonrigid foundation the effect of adding extra mass in a com- pound mounting is broadly similar to that of adding it at the base of a simple 80 Lecture 4 mount, with some additional advantage appearing at very high frequencies. For substantial masses and a light foundation, the secondary resonance peak for a compound mounting appears on the response-ratio curve at a position only a little above that of the foundation with a simple mount and loading mass. The response-ratio curve for high secondary masses is rather less smooth at high frequencies than that for the simple mount with added mass, but, as indicated above, this disadvantage may be more apparent than real. Figure 4.13 represents a comparison due to Snowdon [9] of various methods of mounting on a light foundation beam of low damping, and employing an added mass of 0.2M. The "hevea" mount referred to is of a representative vulcanized natural rubber, while the "parallel" mount uses this rubber in parallel witha section of a high-damping polymer as discussed insection 4.3 above. On balance it appears that the simplest and broadly the most effective technique in these circumstances is to use the simple mounting with a substantial mass at its base and moderate damping to minimize the foundation and mount resonances. A fourth method of employing extra mass to minimize vibration is to attach this mass via a damped spring to the primary vibrating mass. If the added mass and spring are tuned to some resonance frequency of the primary system, then they absorb energy strongly at this frequency and so help to suppress the reso- nance of the primary system. The device is normally termed a dynamic absorber. Its behavior has been considered by a number of investigators, and Snowdon [12] in particular has recently examined the values of tuning and damping which give optimum suppression when various types of idealized viscoelastic media are used for the absorber spring. Figure 4.14 shows atypical set of transmissibility curves which he derived for the system shown in Fig. 4.11b. The secondary mass M, is attached via a spring with viscous damping to the spring-mounted main mass ™,. Curves are plotted for various values of mass ratio p = My/(M,+ M2). Thus, for example, »='% corresponds to M,;=M>2. It is seen that, owing to the frequency selectivity of the device, the use of relatively large absorber masses (a) (b) Fig. 4.11. (a) The compound mount and (b) the dynamic absorber. G. G. Parfitt 81 40 30 20 -20 -40 TRANSMISSIBILITY , T (db) -60 -70 SIMPLE MOUNTING COMPOUND MOUNTINC -90 “100 ! 5 10 50 100 500 1000 FREQUENCY (CPS) Fig. 4.12, Transmissibility of compound mounts using rubber springs [10]. (with the appropriate optimum damping value) can lead to a suppression of the main resonance comparable with that achieved by heavy damping of the main spring mount, but without the loss of isolation at high frequencies which the latter causes. Snowdon has also shown that a further improvement in per- formance can be obtained by replacing the viscously damped absorber spring by a viscoelastic material having a high and constant damping factor and a modulus which increases quite rapidly with frequency. Such a material is quite practical to realize. At frequencies well above resonance, the absorber mass remains almost stationary and the performance of the system becomes virtually independent of its presence. If the three cases considered in Fig. 4.14 has been compared on the basis of a common stiffness in the main spring instead of a common resonance frequency of the complete coupled system, then the system trans- 82 Lecture 4 RESPONSE RATIO, R (db) HEVEA MOUNTING IN SIMPLE SYSTEM SUPPORTED BY MASS LOADED FOUNDATION , m/M= 0.2 HEVEA MOUNTING IN COMPOUND SYSTEM , B= 0.2 ----HEVEA MOUNTING IN SIMPLE SYSTEM, m/M= 8-0 PARALLEL MOUNTING IN COMPOUND SYSTEM, B=0.2 -100 | 5 10 50 100 500 1000 FREQUENCY (CPS) : Fig. 4.13. Comparison of various mounting systems on a resonant foundation. missibility curves would have coincided at high frequencies with each other and with that of an undamped simple mounting system. In view of this it is not to be expected that the dynamic absorber as described would offer any additional G. G. Parfitt 83 protection against foundation resonances occurring well above the main resonance frequency of a spring-mounted equipment. However, the device might well be considered for use attached toa foundation beam at the base of the main mounting spring, or elsewhere. A detailed study of this case has not yet been made. 4,5, SUMMARY A review has been given of the performance ofthe simple resilient anti- vibration mounting and of means of improving its performance, particularly when it is set upon a foundation which is nonrigid, by addition of damping or mass to the system. It appears that, by suitable choice of mount materials or arrangement, a fairly good compromise between low resonant peaks and good high-frequency isolation can be obtained. Damping of the foundation members may be useful but only at and near the frequencies of foundation resonance. The addition of substantial masses to the system as force barriers can be beneficial. Probably the simplest method to reduce the excitation of a foundation by this means is to attach the mass to the foundation at the base of the mount. The mass needs to be larger than that of the foundation to have a substantial effect. Although addition of large idle masses in a ship is not an appealing idea, it may occasionally be possible to use for the purpose the mass of other equip- ment which is already present. (db) BROKEN CURVES REFER TO THE SIMPLE MOUNTING SYSTEM. DAMPING OF THE VISCOUS TYPE TRANSMISSIBILITY mCON 02 05 | 2 5 iO FREQUENCY RATIO y Fig. 4.14. Transmissibility of the dynamic absorber with viscous damping [12]. 84 Lecture 4 4.6. ACKNOWLEDGMENTS ‘The author is indebted to Dr. J.C. Snowdon and to the Director of The Uni- versity of Michigan Institute of Science and Technology for permission to repro- duce Fig, 4.13. REFERENCES 1, J.C. Snowdon, "The Choice of Resilient Materials for Antivibration Mountings,” Brit. J. Appl. Phys., Vol. 9, 461-469 (1958). 2, J.N. Macduff and J.R. Curreri, Vibration Control (McGraw-Hill Book Co., Inc., New York, 1958). 3. C. E. Crede, Vibration and Shock Isolation (J. Wiley and Sons, New York, 1951). 4, J.P. den Hartog, Mechanical Vibrations, 3rd ed.-(McGraw-Hill Book Co., Inc., New York, 1947). 5. R.E.D. Bishop and D.C. Johnson, The Mechanics of Vibration (Cambridge Univ. Press, Cambridge, 1960). 6, J.C. Snowdon, "The Reduction of Structure-Borne Noise," Akust. Beih., Vol. 6, 118-125 (1956). 7. J. Heyboer, P. Dekking, and A, J. Staverman, "The Secondary Maximum in the Mechanical Damping of Polymethyl Methacrylate: Influence of Temperature and Chemical Modification,” Proc. Second Inter. Cong. on Rheology, Oxford, Vol. 26 to 31, 123-133 (1953). 8. J.C. Snowdon, “Reduction of the Response to Vibration of Structures Possessing Finite Mechanical Impedance, Part I,” Rep. 2892-4-T, Fluid and Solid Mech. Lab., Willow Run Lab., Univ. of Michigan (November, 1959). 9. J.C. Snowdon, "Reduction of the Response to Vibration of Structures Possessing Finite Mechanical Impedance, Part II," Rep. No. 2892-T, Fluid and Solid Mech. Lab., Willow Run Lab., Univ. of Michigan (January, 1960), 10. J.C. Snowdon, "Reduction of the Response to Vibration of Structures Possessing Finite Mechanical Impedance,” J. Acoust. Soc. Am., Vol. 33, 1466-75 (1961). 11. R.N. Hamme, Handbook of Noise Control, C.M. Harris (ed.), Chapter 14 (McGraw-Hill Book Co., Inc., New York, 1957). 12, J.C. Snowdon, "Steady-State Behavior of the Dynamic Absorber," J. Acoust. Soc. Am., Vol. 31, 1096- 1103 (1959); and, "The Steady-State and Transient Behavior of the Dynamic Absorber," Rep. 1941-3-F, Willow Run Lab., Univ. of Michigan (November, 1958), DISCUSSION PROFESSOR T.S. KORN drew attention to the usefulness of the concept of mechanical impedance or of electroacoustical analogies generally in the study of mechanical vibrations. He emphasized the importance of the behavior of elastic mountings when the input impedance of the base is reactive and not in- finite. He discussed the concept of the transmissibility factor as the ratio of forces and the possibility of using the velocity ratio or the concept of apparent power transmitted to the base. DR. PARFITT: I, personally, find the use of mechanical circuit elements of considerable help in visualizing and sometimes in idealizing the behavior of a complex mechanical system, but their application does not, of course, alter the problem or otherwise assist in its solution. The same is true of represen- tation in terms of equivalent electric circuit elements, though there is, here, at least the possibility of actually building the electrical equivalent network and making with it electrical measurements which are often simpler than the analo- gous mechanical ones. : I certainly agree that calculations such as are given in the paper do not tell the whole story of sound emission from a ship. What has been presented is an attempt to isolate one aspect of the whole complex problem of noise trans - mission from engine to sea and to see what factors in it are the significant ones, at least in idealized cases. The beam foundation considered in the paper would in practice be attached at its ends to further members of finite impedance G. G. Parfitt 85 through which vibrational energy would escape to the ship's outer structure. These terminations would modify the resonance frequencies and damping of the beam and, if they represented tight couplings to further resonanting systems, could introduce further resonances. However, it does not seem likely that these changes would invalidate the general ideas enunciated. Accordingly, it seems reasonable that almost any measure of the beam's motion or of the force upon it can be employed when one wishes to estimate the change in the final noise radiated due to the isolating measures considered. I would admit, however, that although response ratio as used in the paper provides accurate values for the effects of inserting an isolating system, it is probably safer, owing to certain slightly misleading characteristics mentioned in the paper, to calculate the end-to-end transmissibility (e.g., force on beam over force applied by machine) for each case in reviewing the over-all performance of the system. MR.S. BYARD emphasized the importance of the mechanical impedance concept in assessing the performance of resilient mountings. He asked the lec- turer to comment further on the use of nonlinear springs to reduce the natural frequency of a mounting system for a given deflection under static load. Mr. Byard pointed out that Dr. Parfitt had suggested that the over-all weight of a compound mounting might be kept down by arranging that the intermediate mass comprise in part at least some of the auxiliary components associated with the main engine. He thought it would be dificult to ensure that such an in- termediate load behaved as a true mass andnot as a complex resonant structure. Regarding the question of force "pick-ups," Mr. Byard said that there was no real difficulty in constructing pick-ups which effectively measure force and, in the practical measurement of the mechanical impedance of a structure, sucha pick-up is used in conjunction with a velocity pick-up. DR. PARFITT: Mr. Byard is very right to questionthe practicability of using auxiliary equipment for the loading masses considered in the paper. The main requirement here is that the loading be masslike in impedance over the fre- quency range where foundation resonances are important. Inasmuch as founda- tion beams may be relatively long, and hence of low frequency, whereas items of equipment may be relatively compact, there is a possibility of achieving this limited requirement. However, every individual case must certainly be treated with great care and on its own merits. I have not had any personal experience with nonlinear spring mounts for reducing resonance frequency. I understand that they have been used successfully in large engineering installations, though I suspect that for mobile ship-borne and service use they may be a little critical in adjustment and maintenance. Dr. F.M.V. FLINT said that the question of the advantages of the equivalent circuit approach to the analysis of structural vibrations merited further dis- cussion. He pointed out that with underwater radiated noise, it was not so much the disturbance of the base ofthe mounting which was of interest; for the ultimate current-carrying network (in the electrical analog) was the entire surrounding medium and one wished to know the energy dissipated in the resistive element 86 Lecture 4 of that medium. If the disturbances of the base followed a simple pattern, i.e., a piston motion, the medium could be represented by a very simple pendent net - work. In ships, the base was liable to be stimulated into a very complicated pattern which might be significantly influenced by the existence of the outside medium. Dr. Flint did not see clearly, however, that to resort to electrical analogs was going to give any clearer qualitative understanding of the problems involved in reducing energy transmission into the medium or any greater facility in quantitative analysis of particular situations. PROFESSOR R. E.H. RASMUSSEN complimented the lecturer on his clear exposition and wondered whether he had studied the effect of mechanical dis- turbances, due to traffic, on the stability of laboratory instruments. He also asked Dr. Parfitt for practical results obtained by using mechanical isolating mounts. DR. PARFITT: Unfortunately, I have no figures on vibration caused by traffic. Actual field results on the benefit obtained from isolation systems are very difficult to come by since comparable before-and-after measurements are hardly ever possible. I have no reason, however, to think that the simple theory is not applicable, except insofar as the foundation impedance is not usually well known. LECTURE 5 A SING-AROUND VELOCIMETER FOR MEASURING THE SPEED OF SOUND IN THE SEA M. Greenspan and C.E. Tschiegg National Bureau of Standards Washington, D.C., U.S.A. 5.1. INTRODUCTION The so-called sing-around velocimeter is by now a well-established instru- ment used mostly for the in situ measurement of the speed of sound in the sea and other natural waters. It has been applied to a lesser extent to measurement problems in the laboratory; there is reasonto believe that with suitable modifica - tions the laboratory use of the instrument could be greatly extended. The instrument is automatic, has fast response, and is easily adapted to recording. The models with which we are here concerned are restricted to use with liquids which show no appreciable frequency dispersion except possibly at very high frequencies. They must be designed, adjusted, and calibrated for a particular class of liquids within which the total variation of the speed and at- tenuation of sound is not too large. These changes are commonly caused by changes in temperature, pressure, or composition. The velocimeters have high stability and are therefore especially adapted to differential measurements, such as that of sound—speed gradients in the sea. Other examples of differential measurement are the determination of the effect of dissolved air on the speed of sound in water [1] and the measurement of the temperature coefficient of the speed of sound in water near the turning point (approximately 74°C) [2]. 5.2. GENERAL CONSIDERATIONS A sing-around velocimeter is outwardly similar to the ultrasonic delay line employed in digital computers for information storage. It may be thought of as a cylindrical tank the ends of which are electroacoustic transducers, and the whole filled with the liquid under test. A voltage pulse is applied to the "sender," and a corresponding pulse of sound travels through the sample liquid and is received and converted to an electrical pulse by the receiver. In order to define uniquely the time interval between the pulses and to specify their location in time, some characteristic must be selected that will still be recognizable after the pulse has been distorted by transmission through the liquid and by the bandwidth limitations of the transducers. In the present instrument, the pulse position is specified by the instant at which it begins to rise from the noise. 87 88 Lecture 5 This choice has several important consequences. To begin with, a pulse-modu- lated carrier has now no advantage over the much simpler video pulse even though the distortion of the former would be much less* Further, it becomes essential that the pulse rise rapidly. This is no problem so far as the input pulse is concerned, but the output rises, relatively, very slowly. The fast rise is restored by amplification; nevertheless there is introduced an unknown delay equal to the time which the output pulse spends below the noise. This delay depends on the attenuation characteristics of the liquid. It is primarily for this reason that the velocimeter must be calibrated and used ona class of liquids within which the attenuation characteristics are not too variable. The timing is automatic. The received pulse after suitable amplification and reshaping is again applied to the sender; thus the device regenerates and the pulse repetition frequency (prf) depends upon the speedof sound in the liquid and to some extent upon electrical and other delays. The principle is not new. The earliest description we have found occurs ina patent [3] filed in 1937 by Shepard. Similar systems are described in later patents by Kock [4] and by Larsen [5]. The designation "sing-around" appears to have been coined by Hanson [6]. Hanson, Barrett and Suomi [7], and several others (for references see a recent paper by Ficken and Hiedemann [8]) have constructed apparatus similar to that described here. These instruments were not of high precision. A major source of difficulty is the existence of multiple echoes between the transducers. The various sets of echoes, each set arising from a different pri- mary pulse, are not synchronous because of the electrical time delay. Various means of eliminating the reflections have been used. In the case of a straight path, the transducers are tilted slightly out of parallel so that all received pulses but the first are lost in the noise. In the case of a bent path, where the sound is reflected back nearly on itself, the transducers and reflector occupy their ge- ometrically correct positions, but the reflection coefficient is rather small. The first received pulse is attenuated by reflection once and the second three times; the result is that all received pulses after the first are negligible. Hard rubber, Teflon, and perforated metal are suitable materials for the reflector. A bent path minimizes errors which arise from mass motion of the liquid and is preferred for field models, and in the laboratory in cases where a large volume of sample, which necessitates vigorous stirring for maintenance of ther- mal equilibrium, is used. In cases where the liquid is contained in a small tank immersed in a temperature-controlled bath the straight path is satisfactory. The advantages of a bent path are even greater for a doubly bent path with two reflectors. This arrangement, which is used on all recent models, will be described later in more detail. We recapitulate briefly the principle of operation. A block diagram of the sing-around principle is shown in Fig. 5.1. The input transducer is energized by a trigger-type, pulse-forming circuit which produces short fast pulses. This circuit is adjusted to run free ataprf somewhat less than the expected minimum operating prf. The pulses of pressure produced by the input transducer travel *However, the choice of a video pulse restricts operation to nondispersive liquids. An instrument based on a pulse-modulated carrier could, in principle, be usedon dispersive liquids, but at a single frequency only. M. Greenspan and C. E. Tschiegg 89 down the sample liquid in a time //c, where c is the speed of sound and / is the path length. The received pulses are amplified and shaped and are used to syn- chronize the original pulse-forming circuit. If t, is the sum of the electrical delays and the time lost in the noise, the total time delay is jo (1) The prf, f, is measured and perhaps recorded. Both t, and / are obtained by direct calibration with a liquid in which the speed of sound is known. If the velocimeter is to be used in the sea, for example, a suitable calibration liquid is distilled water. Readings of f with distilled water at various temperatures between 0 and 60°C cover the range which would be obtained in the sea where the extremes of temperature are 0 and 40°C and the salinity reaches perhaps 4%. Corresponding to each temperature of the distilled water is a known speed c and an observed prf, f. These determine the unknowns ¢, and 7 in Eq. (1). It is also possible to determine t, by measuring f for two diffexent known values of 1. This method is both more cumbersome and less accurate; the length / in Eq. (1) is only an effective length and is difficult to define in an absolute sense, especially in the case where the receiving transducer is not accurately parallel to a wavefront. 5.3. APPARATUS 5.3.1. The Transducers and the Path An external view of the velocimeter is presentedin Fig. 5.2. The structure on top is a protecting plate for the sound head; when it is removed, the essential parts are as shown in Fig. 5.3. The inner structures are the transducer mounts; on the left-hand mount the transducer is visible; the reflectors are on the peri- phery. The sound ray traverses a zigzag path about 20 cm long. The transducer mounts are fixed in their geometrically correct positions, but the reflectors are adjustable. The proper adjustment is made by trial while observing waveforms on an oscilloscope; once it is attained, the reflectors are locked in place with the cap screws shown. For some applications the reflectors should also be pinned. Good results have been obtained with both x-cut quartz and with ceramic transducers. The latter are now preferred because they operate in conjunction with simpler electronic circuits. The transducers are made as thin as is con- sistent with ease of handling; thicknesses from 0.2to 1 mm are satisfactory, the best value depending on the type of mount. Mounts of the type shown in Fig. 5.3 have become more or less standard. With these are used transducers of barium-calcium-lead titanate (Bag.g9 Cao.12 Pbp,og TiO3), a material not overly sensitive to temperature, devised some years ago by W.P. Mason of the Bell Telephone Laboratories. The discs are 1.25 cm in diameter and 0.66 mm thick, corresponding to a fundamental thickness resonance of about 3.6 Mc, with surfaces flat and parallel to about 25 ». The electrodes are composed of fired-on silver-ceramic paste; the outer (ground) electrode covers the entire area and the inner (hot) electrode is about 6 mm in diameter and has two #30 silver-plated copper wires attached to it with 63-33-4 tin-lead- 90 Lecture 5 TRANSDUCER SAMPLE LIQUID TRANSDUCER PULSE GENERATOR AMPLIFIER FREQUENCY MEASURING EQUIPMENT Fig. 5.1. Block diagram showing sing-around principle. Fig. 5.2. General view of velocimeter. M. Greenspan and C. E. Tschiegg RECEIVER REFLECTOR “ Fig. 5.4. The transducer REFLECTOR TRANSMITTER mounts. 9] 92 Lecture 5 silver solder. The two transducers in each set are oppositely poled for proper operation with the circuit to be described. Ifanother inverting stage of amplifica- tion were added, then the transducers would have to be similarly poled. The transducer mounts are better seen in Fig.5.4. They are hollow and con- tain only the electrical connections and silicone grease (DC-4). The transducers are held in place by the spring retainers shown, but are not cemented or otherwise fastened. The grease is centrifuged into the mount to eliminate air bubbles and the final seal is made using a thin neoprene gasket under the perforated top cap. The ceramic disc is thus under substantially hydrostatic pressure so that there is no tendency for water to leak in at the edges of the disc or to percolate through it. We have never been able to fabricate a rigidly backed transducer, even using heavily plated material especially processed for low porosity, which is completely impervious at pressures above a few hundred atmospheres. The hollow mounts have been repeatedly tested to 1500 atm without evidence of leakage. 5.3.2. The Electronics As may be seen from the schematic diagram, Fig. 5.5, the circuit employs 8 microalloy transistors, all of the same type. The power required is 8 ma at 6.5 v and may be obtained from any sufficiently stable supply. For instruments that are to be lowered to great depths, the most practical supply is a pair of mercury batteries, visible at the top of Fig. 5.6. The blocking oscillator (Fig. 5.5) utilizes a miniature, ferrite-core pulse transformer of one-to-one turns ratio. It is adjusted to run free at about 6 kc, somewhat lower than any synchronized prf which will occur in practice. The blocking oscillator applies to the sender a positive pulse of amplitude about 6 v and width somewhat less than 1ysec. The sendor oscillates briefly at its natural frequency of 3.6 Mc and a corresponding pressure variation is transmitted through the water to the receiver. It is only the initial transient, confined to less than the first quarter-cycle of this disturbance, which is of interest here. Sup- pose the rising part of the positive BO pulse expands the sender, then a pressure wave travels through the water and compresses the receiver. It follows from the piezoelectric equations that the receiver would put out a positive-going voltage if the transducers were poledalike; inourcase, they are oppositely poled and the input to the base of common emitter stage Q1 is negative-going. The amplifier section consists of common emitter Ql, common collector Q2, and common emitter Q3. Stage Q3 is heavily saturated with negative-going output. Detector Q4 rectifies and amplifies; the output is about 3.6v rf positive- going. It also removes mostof the base line noise. The first four stages Q1-4 are intended as a rise-time amplifier; for example, corresponding to an input slope of 5 mv/psec is an output slope of 75 v/usec. The relevant gain in the linear range is thus about 15,000. In operation, however, stage Q3 is heavily saturated, and the output of Q4 is at its limiting value, 150 v/ysec. Note that it is possible to apply the output of Q4 directly to the sender, thus obviating the necessity for stages Q5-8. This arrangement has been tried out in the laboratory. It has the disadvantage that it is not self-starting, and also that one or more independent series of pulses may arise adventitiously. The remainder of the circuit removes these inconveniences. Schmitt trigger 93 M. Greenspan and C. E. Tschiegg *JINDIIO punore-Surs Jo wWieiserp oeUIaYyIS “G's °SIy YANNI LLINHOS -90 yaldiqdWv-€0 €6ENZ a YOLVTIINSO ONINDOTE - 8d YIOOINL LLIWHOS - Sd Y3MO110S YALLINA-zd ; - I4ITd WV -10 y3aAING 950 €-20 ¥OL1935130 - bd 43 Fe, Hlvd GNNOS NOdN saNad3q aniwa * €6€NZ-80 NYHL 10 NiV¥d VWW8-HVWOOS-USEINL TVW AS 9-4 = YIWHOSSNVYL 3STNd JYNLVINIW = 11 ald PywWO! HAL?) 1 94 Lecture 5 Fig. 5.6. Velocimeter with case removed. Q5-6 further cleans up the base lineand removes most of the rf. The output here is a rectangular positive pulse of about 3 v amplitude and 8 psec width. Stage Q7 is an inverting, low-impedance-output power amplifier which produces the negative-going pulse necessary to synchronize the blocking oscillator. It is adjusted to provide a pulse large enough to trigger the blocking oscillator reli- ably, but not so large that there is any possibility of doubling. 5.3.3. Frequency Measurement The input to the frequency measurement equipment istaken from the emitter of the blocking oscillator where a narrow rectangular pulse of amplitude -1 v is available. The prf, which is inthe neighborhood of 7 kc, may be measured direct- ly, but in the case of a very long cable connecting the sing-around circuit to the measuring equipment, as in deep-sea work, the signal is first converted to a square wave (about 3.5 kc) by means of an Eccles— Jordan type of divider. The M. Greenspan and C. £. Tschiegg 95 Fig. 5.7. Sound head of a velocimeter built by the U.S. Naval Ordnance Laboratory. impedance is matched to the cable by an emitter—follower amplifier. For ocea- nographic applications, the cable need only be an insulated single conductor; the sea acts as the return. At the output end of the cable appears an attenuated, nearly sinusoidal wave. This is amplified and doubled. In any case, then, we have to measure small variations in a frequency of about 7 kc. The prf of the system may be measured by any of the standard techniques depending on the particular requirements and the available equipment. In the laboratory an electronic counter is very convenient, but a stable radio receiver tuned to a high-order harmonic (say 200) of the prf gives equally good results. In many field applications automatic operation and/or recording is required. In such cases the multiplied frequency is converted to an audio-frequency which may be fed to an ordinary frequency meter having a dc output suitable for opera- tion of a recorder. The local oscillator is preferably crystal controlled. 96 Lecture 5 5.4. PERFORMANCE 5.4.1. Stability 5.4.1.1. Supply-Voltage and Ambient-Temperature Fluctuations The transistor velocimeters built at NBS exhibit changes in output prf of from 5 to 11 ppm for a 1% change in supply voltage. The effect of ambient temperature changes on the circuit itself is rather small, amounting toa total change in prfof about | part in 35,000 over a tempera - ture interval 0 to 42°C. The thermal expansion of the sound path is more serious. Most of the transistor velocimeters have a base plate of stainless steel for which the mean thermal expansion is 16.4- 10-2 PC. If the standard path length is taken as that at 20°C, thenthe error at 0 or 40°C is about 1 part in 3000, unless corrections for temperature are made. Most users of the instrument require temperature measurements in any case, and their practice is to correct the velocimeter readings for temperature. The base plate can be made of invar, as it was for the dozen or so vacuum-tube type of instruments made before the present instrument was developed. This procedure effectively solves the thermal - expansion problem, but makes it necessary to take steps to prevent the serious corrosion which occurs wherever the invar touches stainless steel and also at tool marks and scratches in the invar. 5.4.1.2. Frequency Stability The term "frequency stability" here denotes the degree to which the prf of the velocimeter remains constant if the speed of sound in the liquid remains constant. In water, the speed of sound is a maximum at about 74°C [2]. At this temperature a variation of 1°C changes the speed of sound by only 13 ppm, and a variation of 0.1°C by only 0.1 ppm. The stability is therefore conveniently measured in water at 74° + 0.1°C; the prf is obtained by counting for ten sec- onds three times a minute. Such a test was made for 6.3 hr on a transistor velocimeter. The data scattered about a line representing a drift rate of 4.7 ppm/hr with a standard deviation of 0.47 count in about 75,500, or 6.2 ppm. Vacuum-tube type velocimeters [9], equipped with an invar path and solidly backed transducers, are better than this. A 10.5-hr run on such an instrument showed a drift of only 0.3 ppm/hr witha standard deviation of 0.72 count in about 153,000, or 5 ppm. In both cases the standard deviation includes the effect of the +1-count inherent counter error, and possibly some errors due to accidental counts. Figure 5.7 shows the sound head of such a velocimeter. Note the singly bent path and the hard rubber reflector. Figure 5.8 shows the construction of the transducer mounts. 5.4.2, Calibration The standard liquid is outgassed distilled water; we use as standard values of c those we measured by a pulse technique in 1957 [10]. The water, rapidly stir- red, is held at each of several temperatures, measured with a platinum resist- ance thermometer, while the prf, f, is measured by counting pulses for 10 sec. Corresponding values of c and fare fitted by least squares to Eq. (1), which we repeat for convenience e eer ea (a) f c M. Greenspan and C. E. Tschiegg TABLE 5.1. Calibration of Laboratory Velocimeters Model TR-2(NBS) Circuit type transistor Path invar steel (316) No. of points 57 9 Temperature extremes, °C 0.8 to 83.2 0.6 to 50.4 Effective length, 1 Value, cm 14.6941 20.4848 St. dev., cm 0.0010 0.0068 Time delay, ¢t, Value, sec 0.7188 0.3713 St. dev., psec 0.0004 0.0464 Std. dev. of 1/ f data psec 0.0018 0.0045 ppm 18 32 Std. dev. of prediction ppm 2.4 11 97 Fig. 5.8. Transducer mounts for the sound head of Fig. 7. 98 Lecture 5 TABLE 5.1]. Calibration of Field Velocimeters Instrument TR-2, No. 2 TR-2, No. 3 4/5/61 | 4/25/61 | 4/5/61 | 4/25/61 No. of points 12 12 12 12 Temp. extremes, °C 11035 1 to 35 1to 35 || 1 to 35 Effective length, 1 Value, cm 20.6141 | 20.6032 | 20.5820 | 20.5897 Std. dev., cm 0.0112 0.0106 0.0062 0.0059 Time delay, t, Value, psec 0.1760 0.2628 0.2785 0.2311 Std. dev., p sec 0.0771 0.0731 0.0430 0.0403 Std. dev. of 1/f data psec 0.0068 0.0064 0.0038 0.0036 ppm 48 46 27 26 Std. dev. of prediction, ppm 14 13 7.8 7.5 This computation yields the time delay t, and the effective path length /. (If the path is not of low-expansion material, the length | in Eq. (1) should be replaced by/,[1+ @(T — T)], where I) is the lengthattemperature T), T is the temperature, and a the coefficient of thermal expansion.) Table 5.1 shows the results for two instruments made at NBS. Again, the oldinstrument is much superior to the new, but the new one is sufficiently accurate for the field use for which it is intended. It should be borne in mind that the uncertainty in f due to the inherent +1 counter error is +10 ppm for the tube model and +13 ppm for the transistor model, and that at the low temperatures, an uncertainty of 0.01°C corresponds to an error of 30 ppm inf. Some interesting calibration data are available fortwotransistorized instru- ments made by NBSandinconstant use for more than two years by the U.S. Naval Electronics Laboratory in San Diego. Mr. K. V. Mackenzie of NEL kindly made available to us some calibration data taken before and after a cruise during which the instruments were subjected to severe treatment in a storm so violent that it was barely possible for the crew to work. The results are given in Table 5.II. Note that these instruments are roughly equivalent to the TR-2 instrument used only in the laboratory. The differences in 7 and +, barely exceed the standard deviations and are probably not highly significant. For these calibrations the counter errors and the errors in temperature measurement are probably insignificant. 5.5. HISTORY AND DISTRIBUTION The earliest mention we have found of the sing-around principle is in the US patent [3] filed in 1937 and granted in 1943 to F.H. Shepard, Jr., of RCA. As mentioned in a FIAT review [11], Freund and Hiedemann filed a German patent application in 1940. Shortly thereafter, in 1941, W. Kock, then of the Baldwin M. Greenspan and C. E. Tschiegg 99 Piano Company, filed for a similar US patent; this was granted in 1946 [4]. Huntgren and Hallman [12] discussed possible applications to radar (they used the term "ring-around") in 1947; in the same year, M. J. Larsen [5] filed for a US patent, granted in 1949, covering a sing-around echo-location system for the blind. In 1948, R.D. Holbrook [13], working at Brown University, made what so far as we know was the first serious laboratory application of the principle; this was for measurement of small changes in the speed of sound in solids. It was in 1948, also, that R. L. Hanson [6] readhis paper, based on Kock's patent, in which the term "sing-around" was coined; and at the same meeting, W.E. Kock and F.K. Harvey demonstrated a system using loud speakers in air. This demon- stration and Hanson's paper introduced the subject to us. Barrett and Suomi [7] in 1949 experimented with a balloon-borne sing-around device for the measure- ment of air temperature. They used a thyratron pulser and a 16-in. path. The electrical time delay was 34 y»sec. Holbrook's work at Brown was continued by Cedrone and Curran [14], who by 1954 had produced an instrument employing a pulse-modulated 10-Mc carrier with an accuracy in liquids of about 0.1%. A much simpler instrument, utilizing video pulses and good to about 1%, was de- scribed in 1956 by Ficken and Hiedemann [8]. Our own work began in 1952 and by the end of the year a prototype model of high stability, described in NBS Report 2702, Jan. 2, 1953, was in operation. The first operational model had a straight path and quartz transducers, and was field tested in June, 1953. This instrument was used by the Chesapeake Bay Institute for several years. All succeeding vacuum-tube velocimeters, of which more than a dozen were built, had ceramic transducers and a singly bent path with a reflector of hard rubber or perforated metal. These were described in 1957 [9] but were first announced in 1955 [15]. The transistorized version was developed in 1957 to meet the need for a deep-sea instrument. At the present time (August, 1961), 65 of these instruments have been manufactured and we know of current invitations to bid on 61 more. Of the 65, three were made by NBS, two by US Coast and Geodetic Survey, two by the Woods Hole Oceanographic Institute, and the remainder by three different commercial manufacturers. Two instruments are in England, two in Norway, one is at the Saclant ASW Research Center in Italy; most of the rest are owned by various naval or oceanographic installations in the United States. In addition, about 25 instruments are being made with the same sound head but a different timing mechanism. There are also three instruments with a 10- cm path for 1'4-v operation. In 1958, A. Lutsch of the NPL ofthe Union of South Africa reported on an in- strument [16] similar to that of Cedrone and Curran [14], but of much higher accuracy. 5.6. ACKNOWLEDGMENTS We are indebted to our section's shop support group headed by Henry A. Schmidt, Jr., and particularly to Marshall A. Pickett who performed many of the necessary pressure tests. The initial phases of the work were supported by the Office of Basic Instru- mentation of NBS. After 1952, most ofour support came from the ONR. Numerous 100 Lecture 5 field tests were performed by the Chesapeake Bay Institute of Johns Hopkins University (Martin Pollack), by the U.S. Navy Underwater Sound Laboratory (Harry Sussman), and by the Woods Hole Oceanographic Institution (Earl Hays). REFERENCES 1. M. Greenspan and C,E. Tschiegg, "Effect of Dissolved Air on the Speed on Sound in Water,” J. Acoust. Soc. Am., Vol. 28, 501 (1956). 2.M. Greenspan, C.E. Tschiegg, and F.R. Breckenridge, "Temperature Coefficient of the Speed of Sound in Water Near the Turning Point,” J. Acoust. Soc. Am., Vol. 28, 500 (1956). 3. F.H. Shepard, Jr., U.S. Patent No. 2,333,688 (November 9, 1943). 4, W.E. Kock, U.S. Patent No. 2,400,309 (May 14, 1946), 5. M. J. Larsen, U.S. Patent No. 2,580,560 (January 1, 1952). 6, R.L. Hanson, "Applications of the Acoustic Sing-Around Circuit,” J. Acoust. Soc. Am., Vol. 21, 60-61 (1949), 7. E.W. Barrett and V.E. Suomi, "Preliminary Report on Temperature Measurement by Sonic Means,” J. Meterol,, Vol. 6, 273-276 (1949). 8. G. W. Ficken, Jr., and E.A. Hiedemann, "Simple Form of the Sing-Around Method for the Determination of Sound Velocities,” J. Acoust. Soc. Am., Vol. 28, 921-923 (1956). 9. M. Greensapn and C.E. Tschiegg, "Sing-Around Ultrasonic Velocimeter for Liquids,” Rev. Sci. Inst., Vol. 28, 897-901 (1957). 10, M. Greenspan and C, E. Tschiegg, "Speed of Sound in Water by a Direct Method,” J. Research NBS, Vol. 59, 249-254 (1957). 11. E. Hiedemann, FIAT Rev. Ger. Sci., 1939-1946, Part I, 178 (1947). 12. Huntgren and Hallman, "The Theory and Application of the Radar Beacon,” Proc. Inst. Radio Engrs., Vol. 35, 716-730 (1947). 13. R.D. Holbrook, "A Pulse Method for Measuring Small Changes in Ultrasonic Velocity in Solids with Temperature,” J. Acoust. Soc. Am., Vol. 20, 590 (1948). 14, N. P. Cedrone and D, R. Curran, "Electronic Pulse Method for Measuring the Velocity of Sound in Liquids and Solids,” J. Acoust. Soc. Am., Vol. 26, 963-966 (1954). 15. Tech. News Bull. NBS 39, 89 (1955). 16, A. Lutsch, "An Apparatus for Measuring and Recording the Velocity of Sound and Temperature Versus Depth in Sea Water,” Acustica, Vol. 8, 387-391 (1958). DISCUSSION MR. J. CREASE enquired about the effect of dispersion on the velocity of sound in sea water between low and high frequencies and asked whether it was possible to make an estimate of the difference between Wilson's sound velocity data and the phase velocity at low frequencies. MR. GREENSPAN: In reply to Mr. Crease, I have already stated that the principle of operation of the velocimeter is suchthat the readings have a precise meaning only in liquids which are practically nondispersive. In sea water, the only dispersion for which there is positive evidence is that associated with dis- solved MgSO,. As Dr. Sette has pointed out, Fox and Marion* have measured the dispersion in MgSO, solutions by a differential method. Their data could best be fit by a single relaxation process centered at 150 kc, independent of concentra - tion. The total dispersion is about 13.6-1074 parts per mole per liter, and as the concentration of MgSO, in sea water is about 0.028 molar, the total dispersion in sea water should be about four parts in 10°, a value too small for Fox and Marion to detect reliably in sea water itself. If it should turn out that other and larger sources of dispersion exist, as- sociated, for example, with plankton or microbubbles, then new problems will arise. For one thing, most devices which operate at low frequency measure *F.E. Fox and T.M. Marion, J. Acoust. Soc. Am, 25, 661 (1953). M. Greenspan and C. E. Tschiegg 101 phase velocity; but, in many cases, it is the signal velocity or perhaps the group velocity which is desired. In any case, the appropriate velocity will have to be measured at a frequency near that of interest. In view of what has just been said, the second part of Mr. Crease's question cannot be answered at present. MR. L. KAY, in connection with near-field irregularities, drew attention to the work by Christie* on the near-field characteristics of a circular transducer which had been set ringing by an applied impulse. This work had revealed variations in the near-field pattern which are not predicted by continuous wave theory; and, depending upon the position ofthe receiving transducer, the received Signal obtained was of varying wave shape. The fact mentioned by Mr. Greenspan that two instruments did not operate satisfactorily following a slight change in position of the transducers would tendto confirmthis. Mr. Kay, then, commented upon the stress laid by Mr. Greenspan on the use of an impulse rather than a driving wave as being better for the reliable operation of the system. He thought that there would be no difference inthe received signal, since the transducers are free to ring under the damping effect of the water only, giving a 9, say, of 15. Even with an impulse driving force, there will be several cycles of the resonant frequency which in the medium will decay exponentially but at the output of the receiver will appear as a typical rf pulse. MR. GREENSPAN: I believe that Mr. Kay has misconstrued my remarks on the relative merits of a video-pulse and pulsed-carrier drive. The velocimeter operates on the portion of the signal received earliest; what follows the first quarter-cycle is ignored. Either type of drive would give the same result; it is only that use of a video pulse simplifies the electronics. In either case, we have to cope with the fact that the receiving circuit recognizes the leading wave- front somewhat later than it would in the ideal case of zero attenuation and zero noise. Some of this delay is accounted for in the calibration; but there is a vari- able part, associated with the diffraction effects mentioned by Mr. Kay, which remains as a source of error difficult to estimate, but thought to be small. DR. W.N. ENGLISH commented upon the discrepancies in the values of the sound velocities calculated by various methods for the deep ocean. He pointed out that C. D. Maunsell, of Pacific Naval Laboratory, British Columbia, following a suggestion of M. Peterson (San Diego), has compared the observed and cal- culated positions of the first convergence zone for the Kuwahara and Wilson formulations. The former gives a range less than that observed while the latter, even after applying a sphericity correction, gives a greater range by two miles or so. Dr. English said that the discrepancy they have obtained is in the same direction as that found by Hays (Wood's Hole) in his experiments in the Mediter- ranean at a depth of 2200 meters. PROFESSOR T.S. KORN pointed out that in the standing-wave method it was the measured phase velocity of sound which, in certain circumstances, was ob- viously different from the required propagation velocity. *Progress in Nondestructive Testing, Vol. 1. 017 ey " y lune F i 4 : jigs 0} ‘| vi \ y i je Lib f wait} , oa ety iii eo ) 1 Yh hay Py a th ' \ j ‘ aN eta ots (hie mca, H a Af ata st NI aT te : ilies a { re : Ay a ee nh, mua: 8 \( ot br an hs inf iM cin ys aan HEE SAE PN cet A vei a sil eid ayy ee Fateiy Rid ) ran ; i oh WB Wis i POM DAP ITNT og AIT, ee) a ae eT PD Aa eeu) his eS, Um iy ARs Aha ie hk) | DO Chl ea ual. cr Re RRM Mm nee eae deh ( AM sb) ne cline a TN Mee RR TENE Gable WW li ip Nl jae A | bey add I Li pane Fee Cy eee Hai Nise sill ni i { by CO WA Lay Ay hirhy y 1), a, Guat rs ye VO a a i ( ee AN ey ‘ce Gee { deca, bit i ; ' K a i ' Uy ea hs Liny it! nip ney a) ij st m I meee vey Py ae “oahiwiil Uo) riya 7 Nad! Uh ( {’ { { m2 eitan ie: | \ opie r} i i \ OL ryeny Kis i ! TOuT A { ‘ | wird iV red ' iH a ne vat ‘i : ' W ids Vee ai " itt A Ay he i ne jh sprit Mori AUS ORL | ‘ti ag ee tea nl iy ‘bio aT © PNET STV Se RO veh hi ' oa no ik i (9 ie api en ey i ity Au iy : 7 it ii n tra PAD ay Re \ ‘Lie PN OAT IL Hath Oil iialins MORTAR fon nfinjoo’s ‘elt Mile. eve Pokus aybutt’ ee Ee LECTURE 6 UNDERWATER SOUND CALIBRATION STATIONS AT LE BRUSC LABORATORY M.P. Foache Laboratoire de Detection Sous Marine Le Brusc (Var.), France The Laboratoire du Brusc has at its disposal four different calibration sta- tions for hydrophones and underwater sound transducers, each one using a dif- ferent calibration technique. The joint operations of these calibration facilities permit measurements covering a range from 0.1 cps to 100 kcps. Depending on the frequency range to be covered, the following procedures are used: (1) electrodynamical calibration, (2) electrostatic calibration, (3) closed- tank alternating pressure technique, (4) calibration by comparison of filtered noise, (5) pulse technique, and (6) free-field reciprocity calibration. 6.1, HYDROPHONE CALIBRATION The calibration of hydrophones at low frequencies is generally conducted in a range below 1 kc. The hydrophones being of different types, the procedure of measurement depends not only on the frequency range to be covered but also on the hydrophone design. The hydrophones used in the frequency range from 0.1 to 1000 cps have a rigid metal diaphragm vibrating in contact with a piezoelectric element, for instance, a slab of titanate or zirconate ceramic. Electronic calibration is particularly well adapted to this kind of design. The hydrophone used in higher frequency ranges is an assembly of mounted ADP crystals or ceramic elements sheathed in a rubber boot; the elements are either in direct contact or bathed in castor oil which fills the boot. Certaintechniques used with diaphragm -hydro- phones may not be applied to these structures. 6.1.1. Electrodynamic Calibration by Discharge into a Ballistic Galvyanometer The approximate sensitivity of a hydrophone can be measured by the deflec- tion of a ballistic galvanometer when a sudden change of pressure is applied. This pressure variation is produced by applying a weight to the rigid diaphragm. For other types of hydrophones, a decompressional chamber may be used. This kind of measurement, when used for any of several types of production hydrophones, is liable to cause considerable errors, as the capacitance of some kinds of ceramics depends upon the frequency. We are using this method pri- marily for a rapid check of production hydrophones. 103 104 Lecture 6 Générateur THT = Fig. 6.1. Electrostatic calibration. Générateur Générateur Pont dilviseur Mesure HT atténuative rapport] en tension] =1000 Voltmétre a lampes Ampli Préampli Oscillo Mesure THT continue Boite d'atténuation a2 Sh=20 log = -att-k 6.1.2, Absolute Electrostatic Calibration* This is our basic technique adopted forthe low frequency range, and we con- stantly endeavor to improve it. Covering a range from 1 to 1000 cps, it may be used only for hydrophones having a rigid and absolutely plane diaphragm. It works on the following principle: a driving force generated by an ac field is applied between the diaphragm and another plate representing the electrode. This tech- nique is currently used for small standard microphones; it may also be used for hydrophones, but the technological conditions are notthe same. For instance, the diaphragms of our hydrophones have a diameter of 640mm and are 8mm thick. The value of the pressure applied to the diaphragm can be found as follows: if the voltage applied to the plates of a plane capacitor contains a dc component v and an ac component v, we have for the electrostatic force driving the elec- trode, e being the distance between the plates, en 1D) If V is much higher than y, andif the electrode displacements are negligible, we can write ac FE = Fe Vv Denoting the electrode area by s, and the area of the diaphragm by S, the pres- sure due to the electrostatic force is p=—— = Vv 47e? S In practice, we have adopted the following values: M. P. Foach 105 V=1000 v e=1 mm v=100v s=80cm? The signal output voltage developed across the terminals of the hydrophone by this pressure is measured withthe same voltmeter used for measuring v, with the help ofa precision attenuator, inorderto have the same deflection for v as for the signal output voltage. The errors due to the instrument are thus eliminated. The hydrophone response is given by S, = 20 log & — 20 log i attenuation Accuracy of measurement may be affected by fringe effects, but classical cor- rection factors will reduce this effect to a negligible value. The distance between the electrode and the diaphragm may prove to be a limiting factor for the accuracy of the method. This distance being of the order of 1 mm, it will have to be measured with an accuracy better than 0.015 mm in order to avoid a resulting error greater than all the other errors involved. Provided that the diaphragm be absolutely plane, good precision can be obtained by using a comparator. The total error involved in one measurement is less than 1 db. Taking the average of a series of measurements we may assume the error to be less than 0.5 db. The holding device for hydrophone and electrode has to be completely rigid, free from vibration and natural resonance, and it must be set up on resilient mountings. We have mounted this device on aconcrete pillar erected on the rock foundation and isolated from the laboratory building. The upper limit of the frequency range covered by this calibration method is given by the natural resonance of the holding device or of the diaphragm. In this case, free-field calibration will be called for. Basically, this method has no limits in the low frequency region, but in fact ac voltages below 1 cps are not easy to produce. On the other hand, it is not necessary in this range that the driving force be distributed evenly over the whole area of the rigid diaphragm; a drive in the center is sufficient. In this case, simpler mechanical methods can be applied; for instance, stretching a spring periodically by means of a crank. Another method consists of gluing to the diaphragm a coil which is placed in a magnetic field. The driving force being Proportional to the current in the coil, the calibration is easy to achieve. 6.1.3. Relative Electrostatic Calibration In the case of a diaphragm that is not rigid and plane, the absolute electro- static calibration technique does not work but may be applied in a relative way for measurements up to 10 kcps. It then works on the following principle. The electrode surrounds the diaphragm, the latter being made of rubber and having a cylindrical or any other convenient shape. The conductivity of the rubber is assured by a thin coating of silver paint. Although the value of the distance e be- tween the diaphragm and the electrode is not known with an accuracy adequate for absolute measurements, the shape of the frequency curve can be plotted with sufficient accuracy. We use this technique for achieving calibration of the hydro- 106 Lecture 6 Chambre de : H compression AI Oscillo v Voltmétre Y : a lampes — So eeeee—e—eiaeg§w SSS Générateur Préampli WAU |} || | SSSESSSSSSSEE Ampli Générate Boite d'atténuation Ampli continu GM 4531 Philips Enregistreur Kelvin Sh=-1195-att+ 20 log h phones in the 100 to 3000 cps range which cannot be easily obtained under free- field conditions. Free-field calibration is carried out in a range from 2 to 10 keps. It is thus possible, by using the value measured in the 2 to 3 kcps band, to obtain the over-all response between 100 cps and 10 kcps. Provided some pre- Cautions are taken, this method works with a good accuracy. Fig. 6.2. Closed-tank pressure calibration. 6.1.4, Closed-Tank Pressure-Calibration Technique* Although preferring on the whole the method of electrostatic calibration, we also apply the well-known closed-tank measuring technique for occasional checks. Our closed-tank system consists of a small cylindrical tank, thick-walled in order to minimize the excitation by flexure modes. It is filled with water and a small volume of air of known value. The hydrophones having been placed in the water, the air is compressed mechanically by a small piston. This device works in the range below 50 cps. In the very low frequency region (3 cps), the heat ex- change between tank wall and air would call for correction factors to the adia- batic law, but we have never exploited this technique to its utmost limits. We are, however, aware of the fact that other laboratories have succeeded in im- proving this calibration procedure in a very satisfactory manner. In Fig. 6.3 are summarized the results of various methods for the calibration of a H6Tcl-type hydrophone, 6.1.5. Calibration by Comparison Using Filtered Noise The hydrophones used in acoustic ranging are calibrated in the range 2000 to 100,000 cps by comparison witha standard hydrophone calibrated by the reciproc- ity method. The most highly perfected anechoic tank still presents a certain *Figure 6.2. M. P. Fodch 107 Sh en db 1 n i OW OAH i ul Ir AD 100 1000 1 ug f en Hz Fig. 6.3. Comparison of different calibration methods. (Type H6 Tel. No. 23 hydrophone); +Electrostatic Method, @ Electromagnetic method, a Ballistic galvanometer method, x Barymetric method, Voltmetre Méthode de comparaison en bruit Filtre” Analyseur bre Sao (Gas Go hee y dhe thas (ere eolots Ampli 60 db 1-100 kHz Af=250 Hz mpli Bruiteur rotatif 4 billes |- 25 kHz __Générateur de __\ souffle 10 - 100 kHz Fig. 6.4. Anechoic tank with instru- mentation, Hydrophones Tour de directivite standing-wave ratio; therefore the calibrating signal used consists of a white noise which is filtered at the receiving end by a narrow-band filter only wide enough for filtering out the standing waves, Sometimes the noise source is a mechanical set consisting of a rotating drum filled with bearing balls producing a noise in a spectral band from 1 to 35 kcps and sometimes a ceramic projector driven by a white-noise source. The hydrophone to be calibrated and the standard hydrophone are placed successively in the same position, their signals being picked up by a heterodyne analyzer between 2 and 100 kcps. Anautomatic processing device permits simul- taneous analysis and recording of the response curve. 108 Lecture 6 90° 180° Fig.'6.5. Vertical directivity pattern. HP5OAN°OI1 directivité en site These measurements are carried out in an anechoic tank 3.5 m long, 2.2 m wide, and 1.5 m deep. The inner tankwalls are lined with wedges of a cork-and- rubber mixture especially effective in the range above 10 kcps where a reflection factor of less than -10 db has beenmeasured. Figure 6.4 shows the experimental arrangement. A shaft rotating by remote control is used for the recording of the horizontal and vertical directional patterns of the hydrophones shown in Fig. 6.5. By averaging the results obtained by a series of successive measurements, an accuracy better than 1.5 db has been achieved, supposing that the frequency response of the standard hydrophone is known to +1 db. 6.2. TRANSDUCER CALIBRATION For some purposes transducers are calibrated by comparison with a standard transducer using the filtered noise method, but most commonly we apply the pulse technique or the reciprocity method. Measurements are carried out in an anechoic tank 4.60 m long, 3.15 m wide, and 3.15 m deep. ; The inner walls and bottom are lined with the same cork-and-rubber wedges described above for the filtered noise method. The damping value of this lining measured at normal incidence is given by Fig. 6.6 in the range from 8 to 40 kcps. Through the use of this lining the inside size of the tank has been reduced to 3.80 by 2.40 by 2.80 m. M. P. Fodch 109 j He EH SSE arent HH rt fait 15 : # if 3 i see eee Seissetizs fs Ht sf f setae 20 z Ht st ee a ae X = 25 FE i Ht SST Hees : oO =. = z oO +} + 5 See ees 3 i # ce SE it gatas: © 30 a 33 zt & = : £ oa tesa ner 35 3 is es tps + iby i zt i 2 : Ba SHIH: f + z eee ette: te ft ite ee = sas Ht + 3 it +H 0 5 10 15 20 25 30 35 40 Fréquence en kHz Fig. 6.6. Damping value of the tank lining. The tank, shown in Fig. 6.7, is fitted with two movable and rotatable vertical shafts, with weight-handling capacities of 150 and 300 kg, rotated by a servomotor designed to give a bearing accuracy of 0.10°. Because the transducers to be calibrated were of different shapes, a special device for fixing them on the shafts hadto be provided for each transducer. Some of these devices, shown in Fig. 6.8, are designed in such a way as to permit the rotation of the transducer using different rotating axes in order to measure the directivity in several planes. The electronic instrumentation of this test tank is of an all-purpose design allowing complete measurements of transducers, i.e., impedance, response, and directivity. 6.2.1. Impedance Measurement An automatic recorder for complex inpedances, the SEXTA4912, is provided for measuring and recording the value of transducer impedances as a function of frequency. This instrument is of the continuously recording type and has an accuracy of +5%. The impedance—frequency plot is displayed on a CRT screen in the frequency range 5 to 500 kcps in two bands. Positive and negative re- actances from 5 to 10,000 ohms can be measured with this set, and the trans- ducer can bé biased by a direct current during this measurement. An additional device permits observation onthe CRT ofthe parallel reactances and resistances. The remanence of the tube is long enoughto allow the plotting of Kennelly curves. This device may very conveniently be used for matching transformers with transducers by observing the impedance value when the tuning is completed. 110 Lecture 6 APPAREILLAGE MECANIQUE d' EXPLOITATION de la CUVE a) petit chariot b) petit pont c) grand chariot d) grand pont e) selsyn d'orientation f) entrainement des chariots g) volant d'orientation h) frein des chariots i) frein des ponts ) entrainement des ponts ) ) absorbeurs rail du palan i k Dimentions interieures longueur 4570 largeur 3140 hauteur 3150 ; be 4 H L H f H ; } } H H H H : } ma 2 Sese le Fig. 6.7. Schematic of a transducer-calibra- tion tank with fittings. 6.2.2. Principle of the Pulse Method Acoustic calibration of transducers must be carried out in a free acoustic field. When using the pulse method, each single pulse has to be considered as traveling in such a field at the exact moment when it is measured, and it must not be disturbed by interference produced by reflection on the tank boundary wall. This condition imposes a proper separation distance between projector and receiver, and a determined value of pulse length and repetition rate. M. P. Foadch 111 A = Fig. 6.8. Transducer- calibration tank with fittings. 6.2.2.1. Separation Distance In the vicinity of the transducer, intensity fluctuations due to the Fresnel zone do not allow measurement of the sound level. For a plane transducer, with maximum dimension d, the distance has to be more than d?/\ in order to have a discrepancy of less than 3% from the spherical divergence law. Figure 6.9 gives the minimum separation distance tobe used as a function of frequency and transducer size for a given accuracy to be obtained. 6.2.2.2. Pulse Length When the pulse length Tis suchthat T equals 2D/c, where D is the separation distance between transducers and c is the velocity in the medium, interferences due to reflections betweenthe surfaces of transducer and hydrophone are avoided. We have plotted for our measuring tankthe basic diagram of Fig. 6.10 establish- ing a pulse length such that the direct pulse has arrived before the pulses due to reflection. On the other hand, the Q factor of the transducer calls for a minimum pulse length, the duration of the transient state increasing with the value ofQ. The diagram in Fig. 6.11 determines the pulse length for a given value of Q cor- responding to an amplitude equal to 87, 95, and 99% of the signal value on con- tinuous waves. When measuring transducers at a frequency far from the resonance, the pulse length has to be twice as great as that fixed by Fig. 6.11. 6.2.2.3. Pulse Rate Pulse rate must be such as to introduce an appreciable difference from continuous wave measurement. It is therefore a function of cathode-ray-tube remanence or of the integration time constant of the meter. We commonly use a pulse separation of 20 msec for measurements carried 112 Lecture 6 dencm i TTT 2 Tee a OO 2 > « se 7eo7 2 > - Se7e0F 2 aaa 1 10 100 Fig. 6.9. Minimum separation distance as a function of frequency, and transducer size. Ti $41 LLL Ut Be 7 eer 1000 fen kHz Denm 10 out in our tank. This value permits adequate signal integration on a B.K. Level Recorder for a convenient speed of directivity recording. 6.2.2.4. Size of the Anechoic Tank It appears from the diagrams that the tank we now have in use is adequate for transducer measurement at frequencies above 10 kcps, provided that its largest dimension is less than 1 m. In our opinion, the best proportions for measuring tanks are: length equal to 1.5 times the width, and a width equal to the depth. When d is the largest dimension of a transducer to be calibrated and A is the wavelength of the lowest frequency wanted, we choose the maximum separation distance between transducers equal to the width of the tank and to d’/,. If, for example, a transducer with a maximum dimension of 1.5 m has to be measured at 5 kcps, we have d7/A= 7.5 m, and the tank size would have to be 11.25 by 7.5 M. P. Foach 113 2 SS aaa: c E = S 5 E # @ 5 5 2 2 = = £ 5 = 5 3 8 5 BE 2) $ 2 zs PEE ERIE 33 ga arr eg BE e = Sas He i AS a SESE teat tnt SBE je SSS = HEE EEE ETERS es z te HE: fst Hf oF Hes sate re HE 3 Eat Hf = HEHE SESH = +t He H iii f SEH HEHE: HE fait Si jessie eS aE if = be meee ea ED) ea eats ai E TEE F sa: fee b sirieriete ae st HEE sastasel eee teee - = sigzs nesses Ses stones tescsesesiscs SSesress z =e | ettssttt ¢ = i i oa pe SE2E HEEEEEESEES = | eats pakes pespestests est ae ] is : t= Seif {2S SSE sspetss pest as z : tee —— : = = sSyass pesssssse| $ SS = ae 355 ft {ESE + Sy fot +: 33 feast SHEE Resissansisnnnsses este ais Hn isis: nae 33355 tats # fal | i # fat i a5 =: is f HE SE Sass sists Bets = # =f a3 sete 3: aH i pitiists: te + # sf He Siiasitstes sto eeSEE i = + si523 SEE: + Seessiti ees — : Bees eet pet f Sas Hines nantes fea eee i aes = : : = f BE : SSSfE peasee BEE ETH nna fee : 1 2 3 4 Denm Fig. 6.10. Basic diagram plotted for measuring tank, by 7.5m. As a matter of fact, a new tank is to be installed at the Laboratory, measuring 16 by 8 by 8m. 6.2.2.5. Instrumentation The electronic equipment, shown in Fig. 6.12, consists of an ac generator and a broad-band power amplifier delivering a driving power of 1 kw for pulses and 500 w for continuous waves. The frequency range covered is 7 to 27 kcps. A tuned circuit provides the possibility of driving either magnetostrictive or piezoelectric transducers. The power driving the transducer is measured by a voltage divider for very high potentials. Pulses with a length from 2 msec to 1.5 sec are delivered by the generator. The receiver—amplifier is gated to measure only the part of the signal cor- responding to steady state. A B.K. Level Recorder is also provided for plotting signals received as a function of varying elements. In normal or routine measurements, the receiver response is obtained by us- ing two standard projectors, the PP25 and the P30P, their response curve, de- termined by the reciprocity method, being flat enough in the frequency band explored. The receiving standards are the omnidirectional hydrophones BRUSH BM 101 and MASSA M 115 B, the response of which is nearly flat between 1 and 100 kcps. 114 Lecture 6 n 5 6 700 1000 f en kHz Fig. 6.11. Pulse length vs Q for given amplitudes of the signal value on continuous waves. 6.2.3. Application of the Pulse Method for Reciprocity Calibration We will call 7, and 7, the two transducers to be calibrated, 7; being a third auxiliary transducer. Their receiving sensitivities are M,,M,,and ™,; their trans- mitting responses,S,, S$, and S;. To summarize the results: —5 Reciprocity factor, J = ay = Me = 2:10"" Se Sa f Transfer impedance, Z = MS; = MS, = 2 1 where e, is the voltage on T,, e, is the voltage on 7,, and |; is the intensity through 7,. The ratio of sensitivity between T, and T, is M. P. Fodch 115 1) Générateur Bruel et Kjcer 5) Boite d'accord des transducteurs 2) Fréquencemetre Rochar 6) Diviseur T.H.T. 3) Impulseur-cadenceur 7) Voltmetre Philips 6015 4) Ampli puissance Jaubert 8) Ampli réception (500 w en régime continu 9) Philips 6017 | kw en impulsion) 10) Oscillo double trace Cossor Fig. 6.12. Instrumentation for response measurements. Réception i) Emmission T T,) Transducteur emetteur qT Ty 12) Transducteur récepteur 1) Générateur Bruél et Kjoer 7) Ampli 2) Impulseur 8) Voltmetre Philips 6017 3) Thermocouple TH} 9) Découpeur 4) Fréquencemetre Rochar 10) Oscillo a double trace Cossor 5) Voltmetre Philips 6015 11) Enregistreur Bruél et Kjcer 6) Voltmétre Philips 6010 Fig. 6.13. Stand for reciprocity calibration. and Z is obtained by measuring e, and l, R by measuring e, ande,. The block diagram in Fig. 6.13 shows the instrumentation used for these measurements. 6.2.3.1. Calibration by Comparison This is a much simpler calibration procedure than the reciprocity method. We have only to compare the transducers tobe calibrated with a standard model. 6.2.3.2. Directivity Measurements The tank instrumentation furnishes a polar plot of received pulses in db level as a function of transducer bearing and frequency. A 360° directivity diagram can be plotted in two minutes. For special purposes, in order to get complete details about a transducer, we have had to carry out up to 500 directivity meas- urements for different aspect angles in bearing and tilt and at different fre- 116 Lecture 6 quencies. Directivity measurements are used to check off the identity of the different units of a split transducer. 6.2.3.3. Transparency Measurements When designing sonar transducers, it is sometimes necessary to use for the construction of the radiating area a material having a high degree of trans- parency. Materials of this kind are tested in the tank by the pulse method. Tests are also carried out on sonar-dome materials. For this purpose, we use a directional transducer transmitting pulses re- ceived by an omnidirectional hydrophone located ata distance of two meters. The sample is placed halfway between transducer and hydrophone, and the com- parison of the signals obtained with and without interposition of the sample furnishes the transparency value. These measurements can be made at different angles of incidence, while the signal level is recorded as a function of the angle chosen. In this way, we measure rubber, plastic, and steel plates. A convenient size for the sample to be measured is 1 by 1 m. The accuracy of this kind of meas- urement is largely dependent on the way the inclination can be measured. As the results obtained are not very accurate, these measurements have only a relative value, but they are very convenient for comparing various materials. 6.3. TEST-AND-CALIBRATION BARGE MOORED IN THE HARBOUR OF LE BRUSC 6.3.1. Mission The mission of the field station of Le Brusc is to provide a test-and-calibra- tion facility for underwater sound transducers, arrays, and sonar domes under free-field conditions and by continuous wave measurements, on a large scale and more effectively than would be possible in an anechoic tank. Some of the measurements conducted in this barge are: Fig. 6.14. Test-and-calibration barge of Le Brusc. M. P. Fodch 117 4, 5. Fig. 6.15. Sectional drawing of the barge. Primary reciprocity calibration by sine wave or in a narrow band. Secondary calibration by sine wave by comparison with a standard pro- jector. Calibration and recording of directivity patterns of transducers larger than the wavelength where the dimensions of the anechoic tank do not allow working out of the Fresnel zone. Calibration of small transducers where surface reflection due to the small value of the directivity could not be avoided in an anechoic tank. Study and tests of sonar domes. 6.3.2, Physical Features and Layout A pit 30 m long, 15 m wide, and 4.5 m deep has been dredged in the harbor bottom of Le Brusc, and the testing barge, shown in Figs. 6.14 and 6.15, has been moored over it 200 m off shore. This barge has been converted into a test facility by the installation of two test wells permitting a maximum separation distance from projector to receiver of 6.5 m. The barge has an over-all length of 19.10 m and a width of 7.2 m. It has a glass-walled structure covered with a roof, and is divided into calibrating, measuring, and office rooms. For hoisting the transducers and lowering them into the well, there is a monorail carrying a hoist with a weight-handling capacity of 1.5 tons. The wells are surrounded by a gliding rail for measuring instruments. A bridge is mounted across carrying a rolling carriage and a shaft which rotates by remote control, while a polar ink recorder driven by a servosystem records the directivity patterns. By means of this carriage, transducers of up to 1.5 tons can be displaced in all directions, the bearing being adjustable to 14°, while the separation distance between the two shafts is known with an accuracy of 5 mm. Less weighty transducers (up to 300 kg) and projectors to be tested are displayed by two smaller carriages. Another rolling carriage gliding on a rail fixed below the keel of the barge carries transducers for continuous measurement of the acoustic field between 0 118 Lecture 6 setts ae = z uae SE Ee HnE aE Beneanea ec I EH ae a Z eae iui iH Hit iE ERE RHE HR pertte et Hn see iEe fe if HELE = tH Hitt ei got He + ate a fue i Hts a HH 3 Huu fi Sera Besse Hist SSE SER EERSTE HaHEH set insstinses ntttaatt sft if E HH ES if is as Ht Sf 2: + : Soe SSeS — = a3 HE RH 3 i Be Sarat Hest fr ieratintiss fafitntiesicniitianpisteeianiinpsitt 5 STHEEEE assess cee? 3 Oe are ut 2 Ht 5 a sees @ Bf Hi 5 ae : ee 2 +H He 3 HH i 4 = i i ~ i oO sh o 33 2 Ei z A feast HH E tien x RRS se ate ez a alta tf 5 a S2udd bnged pass toss Ht =f esti fi a 8 -l0- SESH EB = SHENG et aa sat HE! is a3 +f + HE gts! Stessssess HH Hy besa suas fae ist iz abs HEH ea testf ett HES # HH EEE eS See eae BEASTS Bea ere ees zee ates RHEE S33 $3 Fi i TEETH Ft i ess 221 sstfsess Ht ES +4] 3 Hss23 333 : i: Het HE # EES ie Fett 3 THinbsstiss SIT ee - i ETE see HEE HAE I ees SS SRS ails if SEES at ates tel Sele eee ceed eee teal ad ee este i iH iH Se Sse Pes sie iH srapatitals O(I m) 5 (1.78 m) 10 (3.16 m) 15(5.62 m) 20 (10 m) Distance en db: re: |m ctest & dire 20 log (rmatres) Fig. 6.16. Acoustic field between two transducers: Panoramic Projector OUM-15 and P30P-209, and 14 m. Between 0 and 20 mthe measurements have to be made point by point. Thus, heavy and large-sized transducers canbe calibrated free from the Fresnel zone. Figure 6.16 shows the accoustic field between the omnidirectional trans - ducer OUM 15 and P30P at 15 kcps. Two concentric shafts are available for the testing of sonar domes. The central shaft carrying the transducer is rotated by remote control in the same way as described above. When studying vertical directivity patterns, depth and tilt of the test transducer can be adjusted by a rack gearing. The standard transducers are checked by reciprocity calibration every three months. They are used in the frequency range from 6 to 34 kcps. The instrumentation is shown in Fig. 6.17. The Test Stand provides facilities for the following measurements: (1) reciprocity calibration, (2) calibration by comparison, (3) field measurements, (4) measurement and recording of direc- tivity patterns, and (5) study and tests of sonar domes. This stand consists of: (1) A Muirhead generator, (2) a 20-w power amplifier, (3) a milliammeter with thermocouple for reciprocity calibration, (4) three Philips voltmeter-amplifiers, (5) a calibration amplifier with an amplifier and a series of octave-band filters covering a range from 3 to 70 kcps. This amplifier can be replaced by another with a bandwidth of 450 cps containing tuning circuits and covering a range from 3 to 50 kcps. The Impedancemeter is used for measuring in the range from 3 to 50 kcps: (1) impedances (R,) up to 500 kohms and (2) capacitances (C,) up to lyf. M. P. Foach 119 Atténuateur de réglage Tension référence eTR TR Voltmetre (GM 6015) (GM 6015) mA thermocouple Y Hartman et Braun 1) Générateur Muirhead 2) Ampli de puissance 20 w (D.S.M./B) 3) Ampli D.S.M./B 4) Filtre d'octave 34 70 kHz (D.S.M./B) q Hydro Emission [] Hydro Réception Fig. 6.17. Instrumentation on the barge of Le Brusc. 6.3.3, Electrical Installation Power of 9.5 kv-a is provided by electric supply from the shore through a submarine cable. 6.3.4, Water Depth One limitation on measurements is imposed by the water depth under each well area available for the realization of free-field conditions. By way of il- lustration, Fig. 6.18 shows some field curves measured at various frequencies between standard projectors P30P. It can be said that the test andcalibration barge of Le Brusc provides means for precision measurements in a frequency range down to 6 kcps. 6.4. TEST-AND-CALIBRATIGN BARGE OF THE LAKE OF CASTILLON 6.4.1. Introduction: History The enlarging of the field of underwater acoustics research by measurements in the low and very low frequency range emphasized, several years ago, the necessity of an acoustic range suitable for these frequencies. As it had not been possible to discover a point along the Mediterranean coast sheltered enough to make measurements at great depths, the necessity of finding a deep lake became evident. All the natural and artificial lakes in the near and far countryside of Toulon were surveyed during the years of 1956 and 1957, when at last the choice fell on the artificial lake of Castillon. The ambient underwater noise level in this lake is very low, corresponding to sea state zero (-16 db), and a water depth varying from 50 to 80 m can be ob- tained for a test facility afloat in the middle of the lake. The project was studied and carried out by the Repair Group of the Naval Shipyard (DCAN) of Toulon, with the help of the Naval Artillery Section and the General Workshop of the Yard. The steel frame and the floats were sent by rail from Toulon to St. André- les-Alpes, and from there hauled by truck to the improvised assembly yard on the bank of the lake on May 12, 1959. The assembly work and the launching preparations were carried out with all desirable speed by the Société Industrielle Toulonnaise, and the barge, shown in Fig, 6.19, was launched on August 13, 1959. 120 Lecture 6 Niveaux sonores (1 db par carreau) HHH + 26y=5 =4" =3) =2) = 1 Oma 2 EN SY PON? 1 (0.5 m) (Im) Distance en db: re: 1m xe) clest a dire 20 log (rmatres) Fig. 6.18. Acoustic field at different frequencies. 6.4.2. General Description The artificial lake of Castillon was created by a dam erected across the valley of the Gorges de Verdon, 6 kmto the north of Castellane and at a distance of 146 km by road from Toulon. The lake depth varies with the seasons, attaining a maximum of 80 m during December and January and again during June and July, while the lowest depth of 40 m occurs in April and September. The crest of the dam has a height of 85 m. The test-and-calibration barge is moored in the middle of the lake nearly 400 m from the dam in an area measuring 200 by 400 m and corresponding to the lowest bottom level. M. P. Fodch 121 Fig. 6.19. Test-and-calibration barge of Castillon, The mooring assembly consists of steel hawsers and nylon cables going to four buoys which are linked by a chain to four concrete blocks weighing one ton each. 6.4.3. The Test-and-Calibration Barge The barge, constructed entirely of welded steel plates, consists of a roof house erected on a platform borne by 31 floats, three of which can be used to control the maintenance of a horizontal position. Witha displacement of 110 tons, the barge measures 17 m in length and 14 m in width. 6.4.3.1. General Layout In the interior of the roof house a central hall, equipped with a monorail carrying a hoist, is surrounded by a space divided into office, laboratory, test stand, workshop, and living accommodations. In the back part of the hall, a test well has been installed measuring 9.70 by 2.80 m. It is surrounded by a hatchway 10 cm high, the upper part forming a gliding rail for the testing and measuring apparatus connected with this well. By opening a gate the well can be approached by an amphibious landing craft. 6.4.3.2. Mechanical Operating Gear A mast 20 m high provides the facility for handling long shafts to which the transducers are fixed. Other handling facilities consist of two davits with a weight- handling capacity of 500 kg each and a derrick with a capacity of one ton. The central monorail has a capacity of one ton, but it has been reinforced at the rear end in order to allow the hoisting of transducers weighing five tons. 6.4.3.3. Electrical Installation A transformer station on the bank provides the power by means of a sub- marine cable. The maximum power available is 25 kw. 122 Lecture 6 6.4.3.4. Acoustical Test-and-Calibration Facilities The facilities currently provided allow the acoustical testing and calibrating of transducers weighing less than 5 tons, by means of a bridge with rolling carriage and a hand-operated rotating shaft mounted across the well. The standard projectors used are of the types TP8E, Ik4O, and P3OP, per- mitting a continuous wave calibration down to 1.5 kcps at depths attaining 30 m. The following improvements are already provided for in the budget: 1. Remote control for the training of the shaft 2. Bridge and rolling carriage for the handling of 8-ton transducers 3. A set of two concentric shafts allowing the testing of sonar domes. For the lowering of 8-ton transducers into the well, the structure around the point of suspension will have to be stiffened. The installation of the test-and-calibration barge on the lake of Castillon, at a cost of nearly 300,000 NFr, has provided a research facility where continuous wave measurements and ranging downto1.5kcpsare possible under very accept- able free-field conditions. Systematic studies are under way to improve the measuring conditions, such as transducer depth, influence of the water level, and so forth. Improvement of the test facilities will have to proceed with a view to making the equipment suitable for the handling of very large transducers and capable of testing them completely and rapidly. DISCUSSION DR. H. A. J. RYNJA commented, regarding the electrostatic method of deter- mining sensitivity, on the measurement of the distance between the hydrophone membrane and the capacitor plate using an interferometer. He thought that a more straightforward method was to measure the actual capacitance of the air gap because the thickness of the gap occurs in the formula for the calculation of the capacitance. This latter method offers some advantages when calibrating hydrophones having a rubber-covered face or a curved sensitive surface. DR. FOACHE: It is certainly possible to measure the distance between the hydrophone membrane and the capacitor plate by a capacitance measurement, but this method does not allow one to check the parallelism of the plates. As the capacitance is a linear function of this distance and the attraction strength a quadratic function, the result may be aslight error if the plates are not parallel. DR. D. SCHOFIELD said that the reciprocity calibration of hydrophones at low frequencies can be made in water-filled rigid tanks. The only measurement required, other than what is normal for the reciprocity technique, is the com- pressibility of the tank, pipes, and contents. This procedure provides a simple means of determining the sensitivity of the hydrophone as a function of the hydro- static pressure. Dr. FOACHE: The reciprocity method for low-frequency measurements is an excellent one, but further work still needs to be done, and it has, therefore, not yet been possible for us to use it. M, P. Fodch 123 DR. D.E. WESTON: During the discussion, mention was made ofatechnique of hydrophone calibration in which the instrument is moved up and down in the water. The method was at a disadvantage if the hydrophone was sensitive to acceleration, but Dr. Weston drew attention to two variants of the procedure, in one of which the problem of hydrophone acceleration did not occur. In this vari- ant, the water, in a suitable container, is moved up and down past the hydrophone when the total acoustic pressure will be dueto the changing hydrostatic pressure plus the known pressures exerted by the acceleration of the water. DR. FOACHE: There are so many methods of calibrating hydrophones at very low frequencies that it would demand too much time to try each of them. The suggestion by Dr. Weston is certainly interesting, but we have never used that method. ol iiiy A wth Pe tee 1 io th Phy aren Ns } Ue ot amet ar pak ye oan es i be TDA A eI A an WITD er Go ist i yey ey CT uae ID an i i | jie Mi } Wh ity x CAM nb ee Me A) rel roe ay nasal Pata! i Wi ai ames tte TU at UN eee Oe aria ea Parl Nea WS site at Wy, } rope Ne Tu Rie ae alety bees MO A A ME ly ig My ; at ea i Hee tik eh Mae ae, . Thi puny ; a i ‘ Spee y bia’ nue 1° APP Aha Ae Win an OL ae SANIT 7) jai T i rei ne et aye een i i j i i | 3 i i i 1 i i i fi { | i i ' ‘i ) i i | ‘i i i i i ( 1 ry ital joey ; i . i ij j { i ‘ = 1 HI i ipa i By s if if i a i Ne et ! i i ie Te aRY ie Vee Hn Wh rat on ii A Le uv iy aoe ae r { ! 1 ee A LECTURE 7 SOME AREAS IN WHICH UNDERWATER ACOUSTICS RESEARCH IS NEEDED H.R. Baker The North Atlantic Treaty Organization Scientific Affairs Division, Paris, France It is with some hesitation that I speak to this group of experts in underwater acoustics on the subject of areas of underwater acoustics where research is particularly needed. Most of you have contributed greatly to the present state of knowledge in this field and will continue to contribute, as the papers presented at this Institute demonstrate. I need not elaborate on the importance of the problem of submarine detection to the NATO Alliance. We are all aware that underwater sound techniques are the only promising means for detecting sub- marines at acceptable ranges. I warn you that my remarks are likely to be biased in the direction of submarine detection, classification, and identification; at the same time, I am aware that the solution to these problems depends upon a basic understanding of acoustic phenomena in the oceans. Almost every area in which I intend to suggest the need for research has been or will be touched upon in talks given at this Insitute, but let us proceed in the hope that I may stimulate your thinking about a few areas where basic and applied research are needed. 7.1. SOUND TRANSDUCERS Basic research on transducing materials should continue, but perhaps we need most to concentrate on the effective use of the knowledge we already possess in this area. First, I must point out that research could profitably be done into the conversion of mechanical energy directly to sound. Hydraulic devices are capable of exerting a great force through a small distance; and this is exactly what is needed, if we can find ways to exert this force in a controlled periodic manner. This approach seems very attractive for low-frequency sound sources because it offers high power capability, ruggedness, and reliability. Large open arrays of transducer elements seem to be the answer to many sonar problems, yet the criteria for designing such arrays to a given specifica - tion are not well understood. Perhaps what is not understood is the interaction between elements of an array when it is driven at high power or when delay lines are used to form and steer acoustic beams. This problem requires both theo- 125 126 Lecture 7 retical and experimental work involving a great many measurements. The number of measurements is likely to be great, and the calculations many and extensive, but modern instrumentation and computers should make the problem more attractive. A few researchers are attacking this problem, but it will require the efforts of the ablest people in the field to obtain the knowledge required for reliable design of open arrays. For some applications it seems desirable to operate transducers at great depth; thus, there is a need to know the effects of high pressures on various types of transducer elements. Calibration facilities for large low-frequency arrays is another major problem. Because of the long wavelengths involved, free-field measurements are not possible at most present-day calibration facilities. Pachner and others have done theoretical work onthe extrapolation of many near-field measurements to the far-field pattern. Another approach is the design of a stable platform for use in deep water, so that free-field measurements can be made. This approach is certain to be very costly and cumbersome. Pachner's work must be carefully evaluated and subjected to experimental test. 7.2, PROPAGATION In the past ten years the use of low-frequency sound which propagates to great distances with little attenuation has stimulated investigations of numerous propagation paths, namely: propagation in surface-bounded ducts, propagation by bottom-reflected paths, by refracted paths to convergence zones in deep water— and in recent years some investigation has been made of propagation paths from deep sound sources. Much of the propagation data is not susceptible to rigid analysis because the conditions under which it was taken could not be rigidly controlled, and it is impossible to simulate the ocean adequately in laboratory tanks. Some facilities and techniques recently developed make it possible to remedy the situation in part. These facilities are fixed, high-power, low-fre- quency sound sources, sensitive hydrophone arrays, and vastly improved signal processing equipment. This equipment, combined with modern recording techniques and electronic computers, makes it possible to collect and process data on a continuous basis. All of this, however, is expensive and will require the cooperation of national governments, navies, and scientists of many nations. For example, underwater sound sources and receiving arrays set up on either side of the English Channel and cabled to shore could be operated on a year- round basis. Properly instrumented, these stations could continuously record signal levels, reverberation levels, and noise background levels, and could correlate them with weather and oceanographic conditions. Data in quantity will make valid statistical analysis possible. Atthe sametime, such a pair of stations could provide a continuous surveillance for the passage of submarines through these narrow waters. Other sets of sound stations in restricted shallow water areas, such as the Danish Straits, the Bosphorous, the Straits of Gibraltar, etc., could provide surveillance of strategic areas andatthe same time yield valuable propagation data to sound physicists. The stations described, of course, could only provide data for shallow water situations. The political and physical geography of Europe is an asset to the NATO nations in the matter of submarine surveillance. To capitalize on this asset, it is H. R. Baker 127 necessary to accumulate data on sound propagation through the shallow waters of strategic locations. These data can best be obtained by a cooperative effort of the nations bordering the waters ofthese strategic areas. Some fixed installa- tions for research purposes are highly desirable. It is entirely possible that information gained from relatively modest fixed installations may serve to guide the development of operational installations. There are several locations near islands where deep-water sound stations could be installed and cabled to shore. From these stations, continuous data on reverberation and noise levels could be recorded. In cooperation with a sub- marine equipped to transmit and receive, transmission loss could be measured over a great range in any kind of weather. Propagation data for the cold water of the North Atlantic, the Norwegian Sea, and the Arctic Basin are meager. While the severe climate would increase the difficulty, fixed stations in these strategic areas could be established; and the data are badly needed. 7.3. SIGNAL PROCESSING Fixed sonar stations can be used for experimental signal processing with little additional equipment. Such matters as signal coherence in time and space can be analyzed on a statistical basis. By careful attention to recording pro- cedures, data can be preserved and distributed on magnetic tape to the various laboratories, where it can be used many times and with different signal proc- essing equipment. Ideas for new research in the area of signal processing will be covered in another paper. 7.4. COUNTERMEASURES A submarine is blind when denied the use of the surface of the ocean and depends upon its ears for information. Little efforthas been exerted in research and development to find effective means to deceive submarines. While acoustic countermeasures in themselves cannot destroy submarines, under the right conditions they can be used effectively to lure them to areas susceptible to attack or to keep them away from convoys or naval task forces. Acoustic tor- pedoes can likewise be deceived and directed away from their intended victims by well-designed countermeasures. Carefully planned work on acoustic counter- measures in peacetime could be of great value in time of war. I have deliberately pointed out areas where international cooperation is desirable in the research and development program. The Division for Scientific Affairs in NATO attempts to stimulate interest and sponsor research in areas where the efforts of morethanone nationare required for achieving best results. LECTURE 8 INTERNAL WAVES J. Crease National Institute of Oceanography Wormley, Surrey, England The intention of this paper is to review our knowledge of internal waves in the ocean, selecting particularly those aspects which may be relevant to under- water acoustics. For present purposes, internal waves may be roughly defined as gravity waves having greater amplitude in the body of the sea than at the sur- face. Noteworthy is their effect in disturbing the lower boundary surface of an isothermal surface layer and the consequent variation in horizontal distance to the shadow zone. Further, the periodic variation in curvature of the isovelocity lines will result in some degree of focusing and defocusing of the sound rays. Lee [1] recently computed the ray paths for a source in an isothermal region overlying another and separated from it by awavy surface. Figure 8.1, from [1], illustrates the resulting variation in intensity. As the height of some internal waves is known to be several tens of meters, it will be of some importance acoustically to discover their properties. Interest in the subject was first stimulated by the observations of Scandi- navian oceanographers at the beginning of the century. The "Fram" expedition a 2m Xx N Z,= 30-8 SIN 300 a ra} re z ao = a ud (a) a \ Z-40-9.| SIN300, 6) \ F ; Sa \ NS {o) 100 200 300 400 500 600 700 800 900 1000 !100 1200 1300 1400 DISTANCE IN FEET (x) Fig. 8.1. Focusing of sound from a source by internal waves on two internal discontinuities. Heavy lines are the interfaces, light lines the sound level (from Lee) [1]. 129 130 Lecture 8 under Nansen's leadership, on approaching the ice edge in northern waters, en- countered the phenomenon of Dead Water, well known to seamen, but not pre- viously investigated scientifically. Ships encountering it found themselves able to make little or no headway. Ekman was able to show with an excellent series of model experiments that Dead Water arose when a ship running into a layer of fresh water overlying salt creates ship waves on the internal interface between the layers; the extra power required to generate the internal waves was sufficient to reduce the headway drastically. It was at about the same time that the repeated use of the more accurate deep-sea thermometers then becoming available indi- cated naturally occurring oscillations within the sea unaccompanied by visible surface displacement. Rather than catalog here the historical record of the subject, it is now pro- posed to give a qualitative account ofthe theory and the most significant observa- tions. Stokes (cf. Lamb [2], p. 370) was the first to consider waves on the inter- face between two liquids of different densities. We need only note here that in a homogeneous fluid there is a unique frequency-wave number relationship o?/k? = (6/k) tanh kh, Which for short waves becomes o*/k? = g/k, and for long waves is o?/k?=gh, where h is the depth of water, o is the frequency, and & is the wavenumber. For a two-layer system on the other hand, there are essentially two degrees of freedom (analogous in some ways to the motion of a double pen- dulum) and the o-k relation is no longer single-valued. In fact, for liquids of almost equal densities the relation factors into o?/k?=g/k, and into o7/k? = gh(Ap/p) for the special case of an upper layer of depth h overlying a deep lower layer whose density is greater by Ap - where h is small compared to the internal wavelength. The first relation is appropriate to ordinary deep-water surface waves and the secondtoa wave with maximum amplitude at the interface. The lat- ter has the appearance of a long surface wave with gravity reduced by a factor Ap/p. This may be seen to arise from the reduced potential energy required to deform the interface between liquids of almost the same density, as opposed to that required for the deformation of the free surface. By introducing successive- ly more interfaces, one may approximate to a continuous distribution of density; and it should be clearthat this will be associated with an infinite sequence of o-k relations. The following equation for the vertical velocity (and displacement) was de- rived by Fjeldstadt [3] in 1933 for an ideal, incompressible, rotating fluid with a continuous distribution of density; the notation is somewhat different from his: 2 4 4 we = fi N2/o? -1 a - Mw -0 (1) where W = p”; we!“*-7 is the vertical velocity (or displacement); the derivatives are with respect to the vertical coordinate z; k and o are the horizontal wave- number and frequency; f is the Coriolis parameter equal to 2Qsin@, where Q is the earth's angular velocity and 6 is the latitude. Finally, N is the Brunt- Vaisala frequency equal to [(g/p)(dp/dz)]”. This is clearly a stability parameter and is the frequency of oscillation ofa parcel of fluid displaced vertically from its position of equilibrium in a gravitational field. The last two terms in the equa- tion are generally small in the ocean and will be neglected in the subsequent J. Crease 131 remarks. For a temperature gradient of 1°C/m, v =4.4-10-? sec”! for 1°C/10m, N =1.4-1072 sec7', The first figure is more appropriate to the diurnal thermo- cline, and the latter to the seasonal thermocline at a depth of 150 ft or so. Together with the boundary conditions, Eq. (1) constitutes an eigenvalue problem. The boundary condition at a flat bottom is W =0 and the same condition may be used at the free surface, bearing in mind that the solutions of most interest in the present context have maximum amplitude in the interior with little deforma- tion of the free surface. Bythis artifice the surface wave solutions are, of course, lost. With the equation in this form it isclear that there is fundamentally different behavior of the solution in different ranges of o. First, if o is greater than the maximum value of WN (i.e., Vmax), all solutions will be of exponential type through- out the depth range; and in view of the boundary conditions this means that in fact no solutions at all are possible. If Nmax >a>f there is at least a range of Z in which the solution is oscillatory, and there is then the possibility of a solution satisfying the boundary conditions. Finally, for of. Eckart [4] (1960) has givena full treat- ment of this eigenvalue problem for a compressible fluid. From these remarks we may conclude that Wand f are upper and lower bounds to the frequencies of free internal waves in the sea, although there are further free oscillatory motions which have periods greater thana week or so which are quasi-geostrophic in character and will not be considered here. Groen [5] in 1948 first drew explicit attention to the upper limit N on the frequency, but there has been little in the way of observations (in the open literature) to confirm it. Only now are the techniques becoming available to make the required observations in deep water at sufficiently close time intervals. An appropriate reference is the paper of Haurwitz, Munk, and Stommel [6] (1958). A long series of temperature measurements were made with thermistors on the sea floor at depths of 50 and 500 m offshore from Bermuda. From Fig. 8.2, a section of the record, it is im- mediately clear that the deep thermistor shows the presence of higher frequen- cies. This is confirmed bythe respective spectra. They both approach a low level rapidly with increasing frequency, and the shallower record differs from the deeper record by a factor of ten. Figure 8.3, showing the variation of W with depth, indicates Mmax at 5th cycles/hr; at the upper thermistor, V equals Yo, while at the lower it is 15/4. It would seem likely that herein lies the explanation of the observed difference in frequency response. Thetwo peaks in W correspond to the seasonal and main thermoclines—often one may also expect a diurnal thermocline responding to meteorological conditions with possibly large values of wv. The development of chains of thermistors at some laboratories, notably at Woods Hole Oceanographic Institution, for rapid sampling of the vertical profile of temperature in the top 400 ft of the sea, would seem to be of the greatest importance in investigating this part of the spectrum. It is possible to make some statements about the velocity of propagation without getting too involved in equations. Fjeldstadt [3] in 1933 and Groen [5] in 1948 treated the analytical details in special cases. At frequencies away from either limit, Eq. (1) becomes 132 Lecture 8 2 w" + ww =0 (2) a and with the boundary conditions will lead to a wave velocity c=WNh/n for the first mode if WM is constant (i.e., c=1/m7[(Ap/p)gh]”, where Ap is the total density variation in a depth h. In the case of the deep thermocline (and sound channel) where large stability is confined to a limited part of the depth, one may expect intuitively that the Ap and the A appropriate to the problem are the change in density and the thickness of the thermocline itself. Thus, if there is a tempera- ture gradient of 8°C between, say, 400 and 1000 m, the velocity is approximately 100 cm/sec, and for an 8°C change at a depth of 50 m (using the simple Stokes formula for two layers), we find thatc=90 cm/sec. There is rather little differ- ence between these two apparently dissimilar cases ofinternal waves, but on the other hand the velocity of surface waves in a total depth of, say, 3000 m is c=2-104 cm/sec, far greater. We shall return to this disparity later. Using this velocity (100 cm/sec), we find the wavelength equal to 31/, km for a wave of period of 1 hr. As the frequency approaches WN the velocity goes to zero. It is on such time and space scales that information is badly needed. The paper of Haurwitz et al. [6] has been referred to, and there is one further set of obser- vations by Ufford [7] (1947) which is of particular interest. He worked with a triangle of three temperature elements moored to the bottom up to 300 m apart. By correlation techniques the phase lag was computed between the records and, hence, the wavelength was deduced. The apparent period of the waves is about 6.8 min, but this is affected by the mean current present. In most cases he was able to explain the o~k relation satisfactorily as the first mode of a simple Stokes two-layer theory or a simple extension of it. Recent progress reports from Scripps indicate that Cox has been getting satisfactory results also. It seems possible that work on acoustic propagation could yield much useful information about the waves (cf. Lecture 16). Alongside the development of experimental techniques there is room for some extension of the theory. The theory has been primarily concerned with the eigen- solutions of the equations. It would seem fruitful to apply statistical methods akin to those now being explored for surface waves in view of the "noisy" appearance of the spectrum and the apparent lack of discrete lines over most of it. There is the added complication that the o-k relation is not single-valued. A further problem is that in many cases, one of which will be illustrated shortly, the disturbance to the isotherms is too large to satisy a linear theory. As with long surface waves, this will lead to change of form and possible breaking. This could well increase the spectrum level at frequencies beyond the upper limit WV (i.e., the region of microstructure). The only other work of which the author is aware regarding the nature of the spectrum will also serve to introduce a discussion of the lower frequencies which are susceptible to observation by repeated dips of a standard bathythermograph. Two ships of the USHO occupied an anchor station to the north of Bermuda and made B/T observations every half hour for the whole period of 25 days. In generai, the spectrum of the fluctua- tions in level (Fig. 8.4) of anisothermdoes not contradict the idea that it may be regarded as noise. However, between 20- and 30-hr periods there is a resolved J. Crease 133 TEMPERATURE °C N CYCLES PER HOUR 1» Se 3 4 5 Nm 500 1000 12 DEC 55 1500 1800, 5 36 37 SALINITY Soo Fig. 8.3. Mean density (o,) and N as a functions of depth (meters) off Bermuda (from Haurwitz et al.) [6]. Lecture 8 *[6] (9Z-M.L OHSN Wo04) ,[[USpueIS uoetedO,, UO UIJeyIosI ue Jo uoNeIzeA yidap jo unmoads samMod ‘f° “BI (sanoy) GOI Ad S9V1 40 ON 09 8s 9S vS 2S OS av OOy be 2p Ov BEM SED rE: zwE OE ez 92 ve 22 oO2 81 EA vi eI_or 8 9 tr z 25 (“LW9 SUNOH N3Aa) -- SONIGV3ad ATUNOH (wNOH svd NINO) — SONIGV3Y ATYNOH (Pass yO $000) (NY) ALISNSG Y3MOd QN3931 134 J. Crease 135 peak. This is more obvious in the correlogram from which the spectrum was made. It is at these longer periods observable by B/T and hydrographic station work that most observations have been made, and there are many reports in the literature of the presence of definite periodicities. Defant [8] (1961) describes a number in which there appear to be semidiurnal and diurnal waves. Anomalies in long oceanographic sections across the sea are often attributed without any direct evidence or justification to the transient effect of the waves. If they are present, they will seriously affect the interpretation of the mean temperature field and, as a consequence, of the acoustic regime as well. The fault of most of these measurements is that they were of relatively short duration, perhaps two or three days, and thus contained only a small number of waves of the suspected period. Haurwitz (1954) has shown, in a statistical treatment of four of the open ocean cases reported in the literature, that only one (by the German research ship Meteor) definitely indicated a semidiurnal tidal component that could not equally well be attributed to chance variations. Eventhough they may be random, these variations of long period are likely to be of considerable importance, as they may have amplitudes approaching 100 m. There are some difficulties inaccounting for diurnal and semidiurnal internal waves. It is natural to look for their cause in the tide-raising force that creates the surface tides but this does not immediately seem possible-the tidal force is acting on the whole body of the fluid, and without some resonance mechanism nothing much is to be expected in the way of internal waves. It has been noted that typical velocities in the midrange of the spectrum are 100 cm/sec, much lower than the speed of the tide, and there wouldn't seem to be much hope of resonance. However, to look at the possibilities, consider again Eq. (1) and note that for waves whose frequency o~f the internal wave velocity is given by the same expression as before except for a factor (1-f?/o)*%i.e., rae rion ceil Rea [ p reer Thus the rotation of the earth implies that for o>f the velocity becomes large and the wavelength long. There is now the possibility of some degree of resonance. However, f varies with latitude and the diurnal tide will strictly achieve resonance only at about 30° latitude, and for semidiurnal tide the resonance lati- tude will be closer to the poles. It is interesting that the USHO [9] observations off Bermuda in 33N should show the possible presence of diurnal waves and no semidiurnal waves. Thus there is no explanation so far for the semidiurnal waves except perhaps in high latitudes. Regarding these, a most significant set of observations were made by Reid [10] (1956) off California (Fig. 8.5). These are the observations referred to earlier in connection with breaking. The semi- diurnal period is very pronounced and the important point is that this record was obtained just off the continental borderland in deep water and records made farther offshore revealed nothing like this regularity. What appears to be happening here is that while the surface and internal waves are effectively un- coupled when moving over a flat bottom, the presence of an abrupt change of depth at the continental slope enables a transfer of energy to take place from the sur- 136 Lecture 8 Os6l “190 Zi 91 ‘(ot] (prey wio43) surrayposi Jo uoneT]I9SO °¢°g ‘Btel €l J. Crease 137 face tide to the internal tide. Rattray [11] (1960) has considered this problem in some detail and given numerical examples. It is perhaps worth quoting Nansen (1909), who said soon after the first observations were made that tidal waves crossing from the North Atlantic into the polar basin across a ridge might be expected to generate internal waves. The presence of semidiurnal waves in open ocean at the Meteor station might now perhaps be accounted for by its location, the mid-Atlantic ridge. Further effects of submarine topography will be found in the production of lee waves. Frassetto [12] (1960), for example, has obtained records with a thermistor chain in the straits of Gibraltar which suggest the possible presence of lee waves. In conclusion, theory suggests that free internal waves will exist in a band of frequencies f mbt aga Mk AON CONCRETE Anne eet eee Bs BOTTOM _ —— Ss. — 430 F M P aa aN 7 A Na Ona ee H 1 | Lv [Seu [B Won bole aaa) ial = : [——— 410 eee eal : : See i EES toccessee Tocoseco 1eeeececese 1200S SSe 109088000 DOC28808O | 430 xcs (Bo Kc/s) 146 KC/S 92 KC/S. re 52-5 Kc/s. | sorBu 22% Tsunrace Boron SCE COMPARISON OF STEEL, CONCRETE, AND RUBBER-COVERED BOTTOMS “~~ 'N FREQUENCY-RANGE 430 TO 25 KC/SEC. Fig. 10.8. B. and K. logarithmic records showing effect of varying the nature of the bottom and the frequency of the sound. either the steel or the concrete bottom is covered with a thin sheet (0.1 in.) of rubber. A further series of records using the concrete tank was made when the bottom was covered with fine sand Op, in. deep in an aluminum tray. These records confirmed that covering the steel sheet or the concrete bottom with thin sheet rubber was equivalent in general features to covering the bottom with fine well- wetted sand free from air inclusions. 10.2.4. Wave Effects Neglecting the case of surface tension waves or ripples and considering only so-called gravity waves, we have two cases: Deep-water waves N= $T?/2n Shallow-water waves d = T(gh)? (A > h) where is the wavelength and T the periodic time of the waves, g¢ is the gravita- tional constant, and hf is the depth of water. In dealing with small-scale waves in the model tank, however, attention has been paid only to the scaling of wavelengths and wave heights. The time factor, involving T and g, has not been considered. 170 Lecture 10 On a model scale, the effect of waves on the water surface in modulating the received sound amplitude is easily demonstrated. A wave 1 m high, full scale, will be 1 mmonthe model scale we are considering. Various methods of generat - ing waves (of lengths lying between 5 and 25 cm) and measuring their height have been tried, and very simple techniques have been used. Shaking the side of the tank proved very satisfactory for generating waves having wavefronts parallel to the line of sound propagation along the tank, while a simple "line- dipper" at the end of the tank would produce waves with fronts at right angles to the direction of sound propagation. A simple and convenient method of recording the wave amplitude and frequency was the use of an air condenser. This con- sisted of astripofmetal mounted parallelto the water surface about a centimeter above it, forming a condenser with the water surface, and varying in capacity as the water waves parallel to the length of the metal strip pass under it. This WEN EV WW a pM Aaa KR ROAK ® SOUND TRANSMISSION IN DIRECTION PARALLEL TO WAVE CRESTS @ SOUND TRANSMISSION IN DIRECTION PARALLEL TO WAVE CRESTS @ SOUND TRANSMISSION IN DIRECTION wave caLiaration PARALLEL TO WAVE CRESTS Imm, Ave ify is a Seas @ SOUND TRANSMISSION AT RIGHT ANGLES TO WAVES @—SOUND AMPLITUDE RECORD $ — WAVE HEIGHT RECORD Fig. 10.9. Modulation of the sound amplitude by surface wives. A. B. Wood 171 arrangement could easily be calibrated by a displacement of the metal strip 1 mm from its normal position above the water surface. Using the double-beam cathode ray oscillograph, records have been made illustrating how waves of small ampli- tude modulate the received sound signal when running with their wavefronts parallel or at right angles to the direction of sound propagation (see Fig. 10.9). Using omnidirectional transducers, as in the examples illustrated, the wave ef- fects are very striking, but are barely observable when directional transducers (4.5°, semiangle) are used. 10.2.5. Temperature Effects Two cases arise: (a) isothermal effects—change of uniform temperature and (b) temperature-gradient effects. In case (a), small changes of temperature, of the order of a few degrees centigrade such as are experienced between winter and summer conditions in the sea aroundthe British Isles, result in correspond- ing changes of sound velocity Cinthe water. At a constant transmission frequency WN this implies a corresponding change of wavelength C/N. The same result may of course be obtained at a constant water temperature by an equivalent small (0) 15-2 @ ss-astc ® Pc WO = 000)» Ga ee = 5 @ 8.7 (gorrom) 92° (sottom) @) 227° (BoTToM) SOUND AMPLITUDE TEMPERATURE RECORD (f° C. CALIBRATION) (© 22.1°c (Borrom) @ aes (sottom) = ((2)_—s9.6°c (soTtoM) Fig. 10.10. Isothermal temperature, and temperature-gradient effects. 172 Lecture 10 change of frequency (wavelength) of transmission. This has been confirmed by making a series of bottom-to-surface records at a mean frequency of 410 kcps and varying by about 1.6 kcps on either side of the mean. The small but definite variation in appearance of the records is equivalent to that which is produced by a total isothermal temperature variation of 3.5°C. This has been verified by experiments in the small concrete tank. In case (b), when temperature gradients are established in the water layer, the first problem is to produce the required temperature gradient. This is simply achieved by inserting an electric immersion heater in the water for the appropriate time, quick stirring, then allowing the water to stratify for a few minutes; the warm water rises to the surface and leaves the colder water in contact with the concrete bottom of the tank. A cali- brated point thermistor mounted near the point transducer is raised from bot- tom to surface with the transducer, and a two-beam cathode ray oscillograph records bottom-to-surface sound amplitude with the corresponding temperature variation (and its calibration marks). Many such records (see Fig. 10.10) have shown that, although changes in the sound distribution occur due to small tem- perature gradients, the records are still much the same in general character as those due to correspondingly small isothermal temperature changes. 10.2.6. Depth of Water Reference has been made earlier to constancy tests of bottom-to-surface records using point transducers, when it was shown that changes could occur overnight when the experimental setup was fixed. After suspecting temperature efiects, small frequency changes, etc., it was eventually demonstrated that a small change of the order of a fraction of a millimeter in a total water depth of about 50 mm could sometimes result in a change of about 30 db in the received signal, both transmitter and receiver having been kept at a constant depth and distance apart, and the wavelength of the sound constant at near 3.5 mm. In pursuance of such observations, a series of records was made in the small con- crete tank to discover the effect of varying the water depth over a much wider range, e.g., from 0 to 5cm maximum depth. In these experiments the bottom was varied from "soft" to "hard" and "absorbent." These three cases were repre- sented by "air" (in the form of rubber mousse cemented to the upper side of a metal-plate sinker), steel, and rubber sheet. In all cases two point transducers are placed a fixed distance apart on the bottom of the tank, and water is allowed to fill the tank slowly (without making waves or ripples) while a logarithmic record of received sound intensity as a function of water depth is being made. Three typical records are shown in Fig. 10.11. Record (a), where the bottom is rubber-covered, indicates a fairly regular series of maxima and minima differ- ing by 20 or 30 db in intensity. It will be noted that at certain critical depths the sound intensity changes very rapidly. Records of this type, the bottom being rubber (sound-absorbent and equivalent to mud and sand) have been made at various frequencies, the spacing of the intensity "crevasses" becoming progres - sively smaller as the sound frequency increases. Records (b) and (c) in Fig. 10.11 were made ina similar manner whenthe bottom was soft or hard. Deep crevasses in intensity level are again observed, occurring muchmore frequently than when the bottom is rubber-covered and sound-absorbent* Such rapid variations of *Note: the frequency is 430 kcps in records (a), (b), and (c). A. B. Wood 173 Cee ee Oe Oat at — 50 -- 49 DEpTH oF BOTTOM 8 WATER (a) “yo FROM OTOSem RUBBER (FREQ. 430 kc/s) a -0 CO OO Cie 8! ! ' ' | fo) ! 2 3 DEPTH 4 CMS 5 4@@@02OZHOHHO88OHO8OOD db - 40 - 30 (b) - 20 SOFT HN oh - 10 ll i} 0 we ee te ee eee 0 5CM @enaeaeeaeeneoeae 2ee0ea2020 C04 db 40 30 (c) a HARD | | 10 ep eee seer ccoccccece. (0) 0 5CM Fig. 10.11. Records of sound transmission over different bottoms (frequency constant at 430 kcps) as the ‘water depth is varied. (a) Absorbent (rubber) bottom, 430 kcps, (b) soft bottom, and (c) hard bottom. sound intensity with very small increases in depth have an important bearing on sound observations in tidal water where the sea level may vary over a range of 10 to 15 ft with the tidal changes. As we have seen, on the model scale a change of depth of the order ofa millimeter, corresponding to a meter at full scale, may result in a change of 30 db in sound intensity at a receiver. 10.3. VISUAL OBSERVATION OF SOUND DISTRIBUTION ON THE BOTTOM AND SURFACE The small-scale observations made so far can only be regarded as pre- liminary and qualitative. A few general pointers have been established regarding the nature of the bottom and depth of water relative to wavelength. The one out- standing feature, however, is the great difficulty of forming a mental image of the general sound distribution in the water. It has become obvious that a very large number of bottom-to-surface records taken at very short range intervals 174 Lecture 10 would be necessary to produce in this way a complete picture of the sound field in a vertical plane along the midline of the 20-ft steel tank. Such a large number of records would take a long time to produce and many disturbing changes could possibly occur during that time, making the resulting very complicated picture untrustworthy. From such considerations as these, the incentive has arisen to find a method which will givea complete and permanent picture of the sound field in the water in the shortest possible time. As a first step in this direction ex- periments were made to obtain a picture of the sound distribution on the bottom, in the hope that a satisfactory technique forthis might give a lead to its applica- tion in midwater. After trying various chemical methods using gelatine-coated plates soaked in dyes and adding bleach to the water in the tank, a much simpler and more effec- tive method was ultimately employed. In this method, and working in the small concrete tank, a false bottom of plate glass or metal sheet is used. This is first sprayed with a thin coat of "water paint" (e.g., distemper, walpamur, etc.) and allowed to dry, but not so long as to set or become bone-dry. The glass plate is then placed in the required position in the water and exposed for a few minutes, sometimes less, to the sound. A quartz transmitter of frequency 250 kcps is Fig. 10.12. Sound pattern on a hard sloping bottom. A. B. Wood 175 used, emitting sound energy at the rate ofabout 5 w (estimated). In a short time, with much less sound intensity than required by the chemical methods, a pattern appears on the surface of the coated glass or metal plate. The most striking results were noticed when one end of the plate rested on the concrete bottom of the tank while the other, remote edge was arranged to be fairly close to the water surface. In this arrangement with a hard sloping bottom, the water forms a wedge above the glass plate. A typical bottom picture obtained in this way is shown in Fig. 10.12. In addition to the primary and secondary beams from the transmitter, parallel interference lines can be seen at right angles to the axis of the primary beam. The more closely spaced equidistant interference lines are due to stationary waves a half-wavelength apart. Attempts made to obtain patterns of the longitudinal (horizontal and vertical) cross sections of the sound beam were not very successful. With certain illuminations of the water surface, however, it was observed that a stationary pattern of parallel lines was visible on the surface of the water. Asthe angle of the wedge formed by the bottom plate and the surface of the water is increased, these interference lines on the surface get closer together and when the angle of tilt is smali the lines are widely spaced. The interference lines occur at intervals corresponding to half-wave increases of water depth and are analogous to the case of Newton's interference rings inoptics. The observations ona model scale just described apply, of course, to the full-scale case in shallow water where the sea bed is sloping. A variable slope in two dimensions could result in the acoustical equivalent of an oil-film optical interference pattern. 10.4, “PICTURE” RECORDS OF SOUND, DISTRIBUTION IN VERTICAL CROSS SECTIONS OF “OPEN” WATER — SCANNING In what follows a description will be given of a method of recording a "picture" of the sound field in the body of free undisturbed water, with sound of relatively low intensity. As a first step, with this aim in view, a series of cathode-ray oscillographic records were made, using point transducers (as described in Sec- tion 10.1 above) to show the distribution of pressure amplitude (a) in a vertical plane and (b) ina horizontal plane along the midline of the tank between the ranges 1 and 2 m (km, full scale) from a point transmitter at a fixed depth. In the first series (a) the point receiver travelled on the midline of the tank on parallel courses displaced vertically at 0.1-in. intervals from near surface to near bottom. These records laid closely together are shown in Fig. 10.13. It will be seen that progressive changes with depth are revealed. A characteristic "V" or "Diamond" structure of the sound field is indicated. (This should be compared with later records made by the method to be described below.) In the second series (b) the parallel courses were in the same horizontal plane in mid- water, these courses being spaced horizontally 1 cm apart up and to + 10 and -—30 cm on each side of the midline. The resulting series of records shows no significant changes from one to another, the sound amplitude on any of the courses being the same as on any other. As a means of delineating a picture ofthe sound field in a cross section of the water, the following method has given very encouraging results and is much simpler and more efiective than the one just described. The new method is es- 176 Lecture 10 Fig. 10.13. Sound distribution in vertical cross sections over a range of one to two meters from the projector. (a) Each scan is made with the transducer at a different depth, the top is at the surface, and each succeeding scan is made at an interval of depth of 0.1 in. (b) Each scan is made at constant depth on a line parallel to the axis of the projector, the center scan is on the axis, the top scan is 10cm on one side, the next-to-bottom scan is 10 cm on the opposite side, and the bottom scan is 30 cm from the axis. sentially a scanning technique which gives a complete picture on a single record of the sound distribution in a vertical cross section of the water either along the full length of the tank or across it at selected ranges. In this method, one of the transducers, either the transmitter orthe receiver, is mounted on the scanning mechanism shown in Fig. 10.14. A metal plate to which it is attached is driven up and down vertically between smooth guides by means of a rotating arm of adjustable length so that its double amplitude of motion in a vertical direc- tion is equal to the depth of the water. The repetition rate at which the trans- ducer moves between the surface and the bottom is under control, an average speed being approximately three times per second in each direction. The motion is adjusted so that the transducer point does not break the water surface nor strike the bottom of the tank. Experiments have shown that the result is the same whether the "scanning" transducer is the transmitter orthe receiver, or whether the scanning mechanism is mounted on the fixed platform near one end of the tank or on the moving platform (trolley) which travels along the rails at the side of the tank. A chain passing over a sprocket wheel connects the rotating arm to the sliding plate which supports the transducer, and the shaft of the sprocket wheel drives the brush contact of a potentiometer which is supplied by a 3-v battery. The voltage onthe brushis amplified and applied to the Y plates of the cathode ray A. B. Wood 177 Fig. 10.14. Scanning mechanism. oscillograph, causing the spot to move upand down on the screen in synchronism and in phase with the transducer point in the water. The received signal is used to modulate the brightness of the cathode ray spot after suitable amplification by a preamplifier and a three-stage tuned amplifier. The hand-operated brightness control of the CRO is adjusted until the spot is barely visible at the surface and bottom turning points whenno soundis being transmitted, When the transmitter is switched on, the cathode-ray spot moving up and down on a vertical line on the screen appears as a series of irregularly spaced bright dots and/or dashes due to the fluctuations of sound intensity as the scanning transducer moves between the surface and the bottom of the water. If now in addition the trolley carrying the receiver moves along the tank, the arrangement of bright and dark spots on the CRO changes according to the position of the receiver. Consequently, ifa record is made by a film moving slowly in a direction at right angles to the line of dots on the CRO screen, while the trolley moves from one end of the tank to the other, a continuous picture is recorded of the whole sound pattern ina vertical section along the tank. It is important, however, if a more or less uni- form density of pattern is required, to compensate for the general decrease of sound intensity with range, due to spreading and attenuation in the water and by reflection at the bottom. This is achieved automatically by means of resistances shunting the output of the receiver preamplifier, one of which is automatically varied by the moving trolley and the other preadjusted by hand according to the circumstances pertaining when a record is to be made. Using barium titanate point transducers, good records can be made by the method described above when the transmitting voltage is as low as one volt. The sound intensity in the water in this case is of course very low indeed com- pared with that which was used to produce the bottom records in Fig. 10.12. 178 Lecture 10 With this new technique numerous records have been made in a study of sound propagation in shallow water. With either the mode or ray theories of propagation, where interference between direct and reflected sound is the main feature, the important influences which must be studied are the depth of the water, the wavelength of the sound, and the ratio of these two quantities; the depth of the source of sound; and the nature of the bottom. Other factors which have already been mentioned, such as temperature effects and state of sea surface and bot- tom, must of course also be considered, but for the present it will be suffi- cient to deal with these main considerations. In the earlier experiments which were described at a meeting of the Acoustical Society of America at Chicago in November 1958 [9], records were made using the sheet steel bottom of the model tank as representative of a flat, acoustically hard, reflecting bottom, and when covered with sheet rubber, as an acoustically absorbent or relatively poor re- flecting bottom. The records obtained, particularly those on the hard steel bot- tom, were very complicated and it was thought at the time that this was partly due to the fact that the steel bottom was not sufficiently flat, irregularities in some parts amounting to as much as 2or 3 mm, i.e., comparable with the wave- lengths of the sound. Since then the bottom has been covered with plate glass ", in. thick of good quality, carefully leveled by ebonite wedges around the edges and made parallel to the water surface by the use of a number of metal cones accurately turned to have heights equal to the water depths required (viz., 2, 1, °4, and '/ in.), the tip of each cone just touching the underside of the water surface. Care was taken to ensure that the space between the plate glass and the steel bottom was water-filled and free from air bubbles. Before making records the water was well stirred, by dragging a long "comb" through it, to ensure isothermal conditions. Scan records have been made covering a wide variety of conditions affecting the propagation of sound in shallow water. As in the point-by-point technique, it was found in the early stages ofthe investigation that there was a very marked contrast in the sound fields according to the nature of the bottom (i.e., acoustical- ly hard and a good reflector like steel or rock, or a poor reflector like rubber or mud and sand). Consequently, when other factors influencing propagation have been examined, e.g., depth of water, wavelength (frequency) of sound, directional properties of transmitter, depth of transmitter, and so on, these have been con- sidered in relation to the nature of the bottom, reflecting or absorbent. The "pic- ture" records of sound fields to which reference is made later therefore generally relate to the variable factor considered as it applies to the two bottom types just mentioned. It will be necessary therefore to refer to the same records in different connections. Most of the illustrations of picture records of sound fields were made with a point (omidirectional) transmitter, but a few are reproduced to show the markedly different characteristics when a directional transmitter is used. The scanning receiver is a point in all cases. Records have been made showing longitudinal vertical cross sections of the sound fields extending to the full length of the model tank, and of transverse vertical sections at a series of ranges from the transmitter. A simple method has been found useful for the intensity calibration of records by the introduction of a series of known db steps in the transmission voltage or in the circuit of the receiver. A. B. Wood 179 Fig. 10.15. Vertical scan over the range from 0.6 to 4,3 m at frequencies of 640, 600, 500, and 400 kcps. Water is two inches deep and the bottom is steel. (4) 400 KC om " = = m 4 m y°) Fig. 10.16. Transverse vertical scan records at d 1-, 2-, 3-, and 4-m range. The bottom is steel, water is 2 in. deep, and the fre- quency is 440 kcps. " nN < m s m vy n d = 4 METERS 180 Lecture 10 10.4.1. Nature of Bottom Reference was made in Section 10.2.3 above to the use on the model scale of sheet steel or plate glass as equivalent to solid rock on the full scale—sup- ported by observations in a model tank having a more realistic thick concrete bottom. Similarly it was found that a sheet of rubber 1 in. thick covering the bottom of the tank had an effect comparable to a layer of fine sand. In what fol- lows, therefore, steel, concrete, and plate glass bottoms are regarded as equivalent to rock and as good reflectors of the incident sound in the frequency range under consideration, while a rubber sheet covering these surfaces cor- responds to a layer of mud or sand under full-scale conditions. When the bottom is acoustically hard (equivalent to rock), and the source is a point, the average scan line of a record consists of, say, 10 or 12 small dots indicating sound-pressure maxima. This confirms the observations made by the oscillographic amplitude-recording techniques described in Section 10.2 above. When the bottom is steel sheet (44-in.), the sound picture as a whole is very complex (see Fig. 10.15), particularly when the depth-to-wavelength ratio is large, e.g., around 20 to 1.. If, however, the bottom is plate glass carefully leveled parallel to the water surface, there is more evidence of regularity in the pattern, a characteristic V pattern being noticeable. There is considerable indica - tion in these hard-bottom records of the propagation of the higher modes, or of many reflections between surface and bottom if we regard the indications in the light of the ray theory. Transverse records at ranges of 1, 2, 3, and4m, in water 2 in. deep at a frequency of 440 kcps with a point transmitter and bottom of steel are shown in Fig. 10.16. These show clear evidence of a stratified pat- tern in the sound field with many maxima in a scan. Fig. 10.17. Vertical scan between 0.6 and 4.3 m at various frequencies. Water is 2 in. deep and the bot- tom rubber-covered. ‘ a es tide | A. B. Wood 181 0.6M (1) 4.3M Fig. 10.18. Longitudinal vertical scan and three transverse vertical scans at l-, 2-, and 3-m range. Frequency is 450 kcps, the water 2 in. deep, and the bottom is rubber-covered, (3) RANGE 2M (4) RANGE 3M When the bottom is acoustically absorbent, rubber-covered (equivalent to mud and sand), and the source is an omnidirectional point, the picture of the sound field is entirely changed. There are now fewer maxima in each scan line—perhaps only two or three dots (or dashes). The over-all pattern is much simpler, but for depth-to-wavelength ratios around 20/1 is still somewhat complicated. Examples of such records are shown in Fig. 10.17. The effect of the sound-absorbent or poorly reflecting bottom is to reduce the number of surface-to-bottom reflections and some of the higher modes are absent. Figure 10.18 shows a longitudinal scan over a rubber bottom, and three transverse scans at ranges of 1,2, and 3 m. The reduced number of maxima is strikingly shown in these records also. Picture records of sound fields such as these serve to show the weakness of the point-by-point method where it was impracticable to obtain more than a small proportion of the data required to plot the complete sound field. By the scanning method the complete picture can be recorded in a matter of a few minutes. 10.4.2, Depth of Water As already pointed out, the effect of varying the depth of the water must al- ways be considered in relation to the wavelength of the sound. The nature of the bottom plays an important part, andthe record obtained depends also on the depth of the transmitter. Many picture records have been obtained in which these factors have been varied. In Figs. 10.19, 10.20, and10.21 are shown three sets of records, the water *sdoy 09S st AQuenbazj ay pue ‘patsA0d-1eqqn1 st uwi0710q ey] ‘deap “ut Q*T SI Isle *sidep quetajgip 1e 1019efo1d yIM UeDS [eOTIIOA [eUIpNITBUOT °*OZ ‘OT “StI 22DjINs Deu Ss Lecture 10 ws. 18-0 uydep 294 lo owes Buluunds 4ay,!uWisudsy $/24 O96 AruUenbeu4 bas8a09 saqqns — wozj0g PSI4DA Yzdap 4ealaceay deep O |-42}0KM 182 *sdoy 09S st AQuanba.zj at pue ‘pataaod-aeqqnt St Wonog op ‘daap ‘ul z St 1a1e\\ *syidep qataypp ie Joioaford yim UedS [eDTIIOA TeUIpMISUOT “6 TOT “BIJ 183 A. B. 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(vi0}0g uD8U) 46-0 4Id9d “Buluupos J33z3}WsudUL Ssp|[B 930jd — wW0330q "s/24% O9gG Asuenbaiy palupa yzdap 4eniscay; deep ,0:1 41270 *doap “ul Z ST Jolem om pue ‘sdoy 99g st Aouenbezy ayi ‘sseys alejd St woloq ay) ‘palJea SI dap IeAtedeI oy $101Defoid Butuueds WIM 9MIDIq “EZ°OT “BIA nfl »6 | wWoyog s02u “294 Vale wc. Buluuodss 4saziwsuds] sspj6 230\d — woxj0g “paluDA Uzdep JeAlez—y doap,Z 1930MKM 5/24 O9¢ A2uanbe.4 A. B. Wood 185 Effect of reducing depth of woter (in /, mm. steps Water Initially 2-0 deep. Wavelength 2°65 mr Bottom rubber 4 plate glas Fig. 10.25. Picture showing the effect of small changes in depth of water. The top picture is for 50 mm depth, and successive pictures from top to bottom made at decrements of 0.5mm. The bottom is plate glass and the frequency is 560 kcps. depths being 2.0, 1.0, and 0.75 in., respectively, when the bottom was rubber covering plate glass on steel. The frequency in this case was 560 kcps and the wavelength 2.65 mm, approximately. Compared with the pattern over a plate glass or steel bottom the 2-in.-depth record over rubber is comparatively sim- ple, but it is nevertheless much more complicated than the records in shallower water, the ratio of depth-to-wavelength in the three cases being roughly 20, 15, and 10. The relatively simple "corrugated" structure of the records in the last two cases is striking and is at present the subject of a mathematical analysis. In another series of records also at 560 kcps the bottom is plate glass overlying the steel of the tank, the depth of water being 2 and 1 in. The charac- 186 Lecture 10 teristic V pattern of the hard bottom is evident in the deeper water. In the records shown in Figs. 10.22 and 10.23, the water is in both cases 2 in. deep and the bottom plate glass. In the first series (Fig. 10.22), the records cover the range of depth from midwater to surface, while in the second series they extend from bottom to midwater. It should be noted that in the first series the range extends from 0.05 to 4.5 m, andthe last record (transmitter near the surface) shows Lloyd's fringes very clearly at the short ranges. In the shallower water record (1 in. deep) shown in Fig. 10.24, the pattern is still complex but shows signs of more regularity than that in the deeper (2 in.) water. It is interesting to notethe changes inthe pattern when small depth changes are made. This is shown in Fig. 10.25, where records have been made in water of depth 50 mm reduced by steps of Wp mm. If a particular feature of the records is selected, for example the inverted V near the 3.5-m mark on the records, it will be observed that this moves slightly to the left with each '/,-mm decrease of depth. Similar drifts to the left are noticeable on other outstanding features, the drift decreasing with decrease of range from the transmitter. A comparable effect is seen in Fig. 10.26, where the wavelength (frequency) is varied in steps. Such records emphasize the relationship which must exist between depth and wavelength in delineation of the sound field. 0.6M (1) 450 KC 4.3M Fig. 10.26. Picture show- ing the effect of small fre- quency variations. Water 2.0 in. deep, the bottom is (2) A425 KC rubber-covered, and the frequency is 560 kcps. (3) 400 KC (4) 450 KC A. B. Wood 187 10.4.3. Wavelength of Sound Assuming the velocity of sound inthe water is constant, variation of frequency will result in a corresponding variation of wavelength of the sound. Many of the earliest picture scan records [9] showed the effect of varying frequency, e.g. in steps of 100 kcps over a range 640 to 400 kcps. Such records, particularly those made over a rubber (sound-absorbent) bottom, showed a marked similarity in general appearance, but it was difficult to trace the transition from one frequency to the next in the series (see Fig. 10.17). When the frequency steps are smaller however, e.g., 400, 425, 450 kcps as in records shown in Fig. 10.26, the change in position on the record of certain clearly marked features can easily be observed. These changes are comparable to those of Section 10.4.2 where the results of small depth changes were discussed. 10.4.4. Temperature of Water The question of the temperature of the water, isothermal and with gradients, was discussed briefly in Section 10.2.5. Many bottom-to-surface records were made by the point-by-point oscillographic technique which showed that small temperature changes had the same effect as small changes of frequency. Thus, around 400 kcps a change in temperature of 3.5°C could be expected to produce the same effect as a change of frequency of 3.2 kcps (i.e., 1°C is approximately equivalent to a 1-kcps change of frequency at 400 kcps). Variation of tempera- ture in the water results in a change of velocity of propagation of the sound and, the frequency being assumed constant, is just another way of varying the wave- length. The frequency (wavelength) effects shown in Fig. 10.26 should therefore be reproducible by a sufficient change of temperature of the water. 10.4.5. Directional Transmission In all the scan records mentioned hitherto, the transmitter has been of the omnidirectional type permitting the propagation of modes or rays in almost all directions. When the transmitter is directional, however, relatively few modes are propagated and the scan picture of the sound field along the model tank be- comes much simpler. A series of four such records, using a 2-cm-diameter transmitter at a frequency of 560 kcps (semiangle of primary beam, 9.3°) in water 5 cm deep, is shown in Fig. 10.27. In record 1 the bottom is plate glass and the directional transmitter is in midwater. It will be seen that this record resembles that of a point source transmitting over a rubber (mud) bottom (see for example Fig. 10.19) rather than that over plate glass (rock). In both cases, of course, the higher modes are suppressed, but in different ways. In records 2, 3, and 4 the plate-glass bottom is rubber-covered, the directional transmitter being in midwater, near bottom and near surface, respectively. Changes in pattern due to these changes in depth of transmitter are apparent, but the gen- eral character of the record is much the same with all three cases, and indeed with that of record 1 when the bottom was plate glass. In Fig. 10.28 the directional characteristics of a transmitter are shown at 1-m range (a) by rotating the transmitter, the point receiver scanning vertically at 1-m range, and (b) by rotating the transmitter, the receiver at 1-m being fixed in midwater. Method (b) is of course the conventional method of recording beam characteristics. The record in (b) represents the intensity variations 188 Lecture 10 SOUND FIELD OF DIRECTIONAL TRANSMITTER IH SHALLOW WATER {Transmitter 2-Qcms. dio. 6=9-30 Frequency 560 kc/s Woter Scms. deep.) 1. Bottom plote glass Transmitter In mid-water. Fig. 10.27. Picture made with a directional trans- 7, Jottom rubber covered mitter. The bottom is plate Transmitter in mid-water glass in the top picture and rubber-covered in others. Water 2 in. deep. 3. Bottom rubber covered Transmitter near bottom 4. Bottom rubber covered Transmitter near surface DIRECTIONAL CHARACTERISTICS of BoTi transmitter (2cms. dia.) (Transmitter rotating uniform ly) (a) Point Receiver scanning verticolly : A : at 1metre range. Fig. 10.28. Directional characteristics of projec- tor. (a) Vertical scan rec- ord, (b) Pressure ampli- tude record at midwater depth, (b) Point Receiver fixed in mid-water. Sound pressure amplitude recorded, A. B. Wood 189 shown by a horizontal midwater line of the scan record (a). The latter shows not only this, but the whole pattern of sound distribution between surface and bottom of the water layer. The stratified character of the transmitted beam and their relative intensities and angular spacings are clearly shown in the original scan records. Figure 10.29 shows a series of nine scan records, the first eight of which show sound fields in vertical sections across the tank at various ranges between 5 and 400 cm from a 2 cm-diameter barium titanate transmitter operating at a frequency of 568 kcps, the semiangle of beam in this case being 9.3°, approximately. The water depth was 2 in. and the bottom rubber - covered. The last (9th) record shows a scan picture along the axis of the pri- mary beam from one end of the tank range (5 to 400 cm) to the other. It is of interest to identify the transverse section scans at the corresponding ranges of the longitudinal scan. The eight transverse records show very clearly the spread- ing of the primary beam and its tendency to stratification in horizontal planes, varying in spacing between the layers according to range from the transmitter. While it is appreciated that the directional transmitters used in these experi- OIRECTIONAL TRANSMISSION. Sound Fields across the beam at various ranges (Recors 8) Scund Fields along the heam 5 to 4O0cms ronge (R, 5 RANGE cms. 20 40 Fig. 10.29. Sound fields across the beam of the directional projector at various ranges. Stems 100 200 700 600 VERTICAL SESK ON AXIS OF PRIMARY SEAN 190 Lecture 10 ments have excessively large diameters on the scale under consideration, they have proved very useful in providing known directional characteristics for cer- tain propagation studies. 10.4.6, Calibration of Scan Pictures of Sound Fields The recorded sound fields illustrating this paper show light and shade pat- terns representing the variations of sound intensity in vertical cross sections of the water. The areas of high intensity are seen as white (bright) spots while those of very low intensity appear dark on the records. There are two possible sources of error in regarding the brightness of the spots as a measure of sound intensity: (1) the motion of the scanning transducer is SHM, and as a consequence undue emphasis is given tothe brightness of the CRO spot and to the photographic exposure at the turning points of the motion near the surface and bottom of the water layer, and (2) there is also a possibility that the brightness modulation by the sound signal applied to the grid of the CRO may not be linear. In the method of intensity calibration to be described, these two unknowns are taken into account to some extent. The record brightness in this method is varied by introducing known changes in the transmitter voltage in 2/1 (6-db) steps or by introducing a db attenuator in the receiver circuit. Typical records of such calibrations are shown in Fig. 10.30. The upper record shows a scan at con- stant range reduced in strength by 6-db steps, the lower intensities being thereby gradually eliminated from the record. The two lower records show the effect of repeating the same longitudinal scan of the tank with a 6-db reduction of signal strength in the second record. The predominant features and over-all character of the records of course remain the same. 10.5. THEORETICAL WORK - FULL-SCALE TRIALS As indicated at the outset of this paper, the theoretical treatment of the complete problem of sound transmission in shallow water, even under idealized conditions, is very difficult. A brief reference was made to the work of C.L. Pekeris, particularly in regard to his development of the mode theory in 1948. More recently T.G. Weale [8] has dealt with the mathematical aspect of the 0 db 6 db 12 db 18 db Fig. 10.30. Intensity cali- bration records. (1) Con- stant range intensity re- duced in 6-db steps. (2) and (3) Longitudinal scan with a 6-db reduction in record 3, om we ? > i ; a “ee 2 heats 9 Nn A. B. Wood 191 250 CMS (a) Computed Chart (for Range 200-250 cms)(Hand Plott ing) CMS Fig. 10.31. Comparison of computed record with measured record. Water is 5.0 cm deep, the bottom is plate glass, and the fre- quency is 560 kcps. 150 225 CMS (b)Computed Chart(for Range 150-225 cms Automatic Plotting) 50 450 CMS. {c) Record made in Model Tank (for Range 50-450 cms ) problem and employing Hankel functions has derived expressions for the spatial distribution of sound intensity ina shallow water layer. Using Weale's theoretical results, K. W. Harrison has, by means of computer techniques, plotted the sound field in a part of a record actually made in the course of the experiments here described. The actual record and computed sound fields are shown in Fig. 10.31. In (a) the theoretical sound field is plotted by hand in the range from 200 to 245 cm while in (b) the theoretical sound field is plotted automatically in the ranges from 150 to 225 cm. The actual record obtained under the conditions assumed in the theoretical computation is shown in (c), covering the range from 50 to 450 cm. The diamond and V structure of the recorded sound field is observable in all the records, and the slope of the V lines is approximately the same in the computed and recorded records when allowance is made for the relative scales of the X and Y axes in the various cases, In this record the bottom was plate glass partly covered by rubber (to remove some of the higher modes), the water was 5 cm deep, the frequency of the sound 560 kcps, and the transmitter situated about 2 mm above the bottom. As a first attempt, this theoretical computation is very encouraging. It has, however, taken a long time and much effort to obtain, and there is clearly much more to do. Full-scale trials are in preparation to try out the scanning technique in the sea. For this purpose suitable transducers and scanning equipment have to be designed and a suitable area chosen for the experiments. All this is taking much time and manpower, not to mention expense, all of which tends to emphasize the advantages of small-scale model experiments. 192 Lecture 10 REFERENCES 1. F.C. Johansen, "Research in Mechanical Engineering by Small Scale Apparatus," Proc. Inst. Mech. Engrs., 151-272 (1929). 2. R.W. Pohl, "Acoustics" and "Optics" (Springer Verlag, Gottingen). 3. D. E. Weston, "Moire Fringe Analogue of Sound Propagation in Shallow Water,” J. Acoust. Soc. Am., Vol. 32, No. 6, 647-654 (June, 1960). 4, A.B. Wood and F.B. Young,"On the Acoustic Disturbances Produced by Small Bodies in Plane Waves Transmitted Through Water with Speical Reference to the Single Plate Direction Finder,” Proc. Roy. Soc. (London), Vol. A 100, 261-288 (1921). 5. F.H. Sanders and R.H. Stewart, "Image Interference in Calm, Near-Isothermal Water,” Can. J. Phys., Vol. 32, 599-619 (1954). 6. R.W. Young, "Image Interference in the Presence of Refraction,” J. Acoust. Soc. Am., Vol. 19, No. 1, 1-7 (January, 1947). 7. C.L. Pekeris, "Theory of Propagation of Explosive Sound in Shallow Water,” Geo. Soc. Am., Mem. No. 27 (October, 1948). 8. T.G. Weale, unpublished theoretical paper, A.R.L., Report R5/Maths 2.26. 9. A.B. Wood, "Model Experiments on Propagation in Shallow Seas," J. Acoust. Soc. Am., Vol. 31, No. 9, 1213-1235 (September, 1959). 11. LECTURE 11 NONSPECULAR SCATTERING OF UNDERWATER SOUND BY THE SEA SURFACE H. Wysor Marsh Marine Electronics Office AVCO Corporation New London, Connecticut U.S.A. 1. INTRODUCTION Marsh et al. [1,2] developed a general theory of sound scattering by the sea surface, and considered the specular reflection in detail, in connection with an analysis of propagation in a surface isothermal layer. Nonspecular reflection can also be important in influencing propagation, and is especially significant in studying reverberation, or back scattering. 11.2, NONSPECULAR SCATTERING For the theory of nonspecular scattering we havea point of departure follow- ing Marsh et al. [2], employing their notation throughout, and using their equation: AQ,p) = [1 = 4 yo? ffm) S(l-a,m - B) dl dm) 5(A - 2) 5(u - B) + 4y?0” SA-2,n - B) The specular term is that involving the brackets, which they denote by Q(A,n) (A — a,p - B) We now define the nonspecular term to be I'(A,u) so that T(Q,p) = 4y20? S(A - a,p — B) (1) To reduce this result, we need the following additional results from the work cited: S (l,m) Lf pr) Jolrd - v?)?\ dr 0 and a 2 h?p(r) =5 { Jo = a 2(@) do and : AA@)) = Gan? exo 26) ousS2 193 = 194 Lecture 11 Writing PealoQoaayr «(a(S we then have (a ie 2.2 ; T(A,p) = Cyk? { i Jo (ee i [r(1 — v')?] exe(=3 Jo tdrdw (2) Let O_-4y ké Then Cnt nent ~ 2g \, -9/2 T(A,n) = an | i, Jo(ur) Jo lr -v' 7)”7] exo( 3). ru dr du Op hs Sf 2-9/4 -2g eral : This result may be more conveniently written as 2s 1 7h T'(,p) = exp [- +)8 (4) py’)? where a=? =f yA Gg In terms of convenient units, we have finally T(Q,p) = 0.098 y2W 75(1 — v!2)-2 exo )a' a a’ = 6.33H~ /°b(1—v'2)% (5) Let & be the angle betweenthe specular direction and the direction of scatter- ing. Then evidently, 1-v?=2-(W-y)?-2cosy (6) .3. BACK SCATTERING In the case of back scattering, v=y, and the angle between the vertical and the direction of the incident wave is ¥/2=6. Thus, for back scattering, 1-v'?=4 sin?6 and Ys 2 i melee, -¥, T, = 0.0061 H’° cos*@ sin” @ exp Buch a! = 12.66 H~”5 bsind (7) where we have written T=I. for this special case (reverberation). In applying this equation to the calculation of reverberation intensities, a number of tech- nical factors, including the geometry of the situation, must be considered. How- H. Wysor Marsh 195 BACK SCATTERING COEFFICIENT, ( F, Feet -/°) to) I 2 3 4 5 6 4 8 ©) 10 WAVE HEIGHT x FREQUENCY PARAMETER,(FH, kc -ft) Fig. 11.1. Back scattering vs wave height and wave height times frequency. ever, certain general conclusions can be drawn. The behavior of reverberation with changes in acoustic frequency and changes of sea condition is completely controlled by the expression Reni ext = ye (8) where T. = 0.0061 cos?6 sin~* 6F. 1.0 mn 9 iis H=8 WAVE HEIGHT, (H, Feet) BACK SCATTERING COEFFICIENT, (F, Feet “/>) as W nN Ol -l 1.0 10 ACOUSTIC FREQUENCY ,(f, Kilocycles Per Second) Fig. 11.2. Back scattering vs acoustic frequency and wave height. 1 _ 196 Lecture 11 Using a value sin@=1 for convenience, we have plotted F against b for fixed H in Fig. 11.1, and F against f for fixed H in Fig. 11.2. Figure 11.1 permits a comparison of back scattering with specular reflection. -4, CONCLUSIONS Figure 11.2 shows the comparative insensitivity of reverberation to wave height and frequency, for the large value of sin@ which corresponds to grazing incidence of the incident radiation. Both of these phenomena have been well known experimentally for some years. We are entitled, therefore, to have some confidence in the theory of sea surface scattering. In addition, the essential features of the sea surface spectrum are contained in I. We, therefore, have some additional confirmation that the Neumann—Pierson spectrum is correct. REFERENCES 1. H.W. Marsh, "Exact Solution of Wave Scattering by Irregular Surfaces,” J. Acoust. Soc. Am., Vol. 33, 330-333 (1961). 2. H.W. Marsh, M. Schulkin, and S.G. Kneale, "Scattering of Underwater Sound by the Sea Surface,” J. Acoust. Soc. Am., Vol. 33, pp. 334-340 (1961). DISCUSSION MR. A.G.D. WATSON thought the work most important and valuable and he was sorry the lecture was so condensed. In his talk, Dr. Marsh had raised many problems in mathematics, physics, oceanography, and underwater sound, but he was only going to comment on the mathematical aspect. He doubted the validity of the lecturer's use of Wiener's theory in the resolution of the reflected field into plane waves, but the final results are unaffected as Dr. Marsh does not employ Wiener's formula in his calculations. The justification of the resolution into plane waves could be, perhaps, carried out by considering a Fourier analysis of the field over a plane on the positive side of the scattering surface. It is not, however, necessary to use Wiener's formula for this purpose, if we follow Dr. Marsh and employ delta functions. Mr. Watson, then, spoke of the second step in the development of the coefficients of the power series in sigma which was also followed, without justification, by Rayleigh and others. Thirdly, there is the evaluation of the coefficients in terms of the correlation function of the surface and this is where, in Mr. Watson's opinion, Dr. Marsh has made a great con- tribution. He had, himself, made a similar approach and obtained the same result. Mr. Watson said that it was difficult to reconcile Dr. Marsh's formula for his function A with results of other workers. Using Dr. Marsh's notation and following a crude argument, assuming a Gaussian distribution of heights on the rough surface, one obtains a specular reflection coefficient of exp (-4y a2) and this agrees, to terms in o”, with Rayleigh's result, for a sinusoidal surface, in terms of Bessel functions. Finally, Mr. Watson asked Dr. Marsh if he would indicate how his formula is reconciled with the conservation of energy, when the film is integrated over all angles. DR. MARSH: Wiener's method is formally applicable to any functions which are invariant under time translation. It is formally applicable to the resolution H. Wysor Marsh 197 of any wave field into plane waves. Wiener's formulas are, in fact, used through- out my development, although a delta function is used for convenience in the final stages, since the power spectrumis more easily utilized than the integrated spectrum. The question of rigor in the use of Wiener's method is another matter. With- out doubt, sufficient qualifications could be made to guarantee validity, except for circumstances of vanishing probability. The fact is that the results are formally valid. It is not surprising that it is difficult to reconcile my results with those of others. Only Rayleigh has results which are comparable, and, then, only for a sinusoidal surface. My results agree with Rayleigh's when compared under equivalent conditions. My results are not comparable to calculations based on the distribution of heights because the height distribution is, in general, not determined by the surface spectrum, and vice versa. A Gaussian surface cannot be sinusoidal and, therefore, any agreement between a Gaussian surface and Rayleigh's results is fortuitous. The important point, as Eckart pointed out, is that the low-frequency scatter- ing is determined by the surface spectrum, and not by the height distribution. My formula shows that energy is conserved, since the negative integral of the nonspecular scattering over all direction cosines plus the specular term is unity. DR. H. CHARNOCK asked the lecturer whether there was any evidence that the so-called "equilibrium sea" is horizontally isotropic. DR. MARSH: I do not know whether the equilibrium sea is isotropic. How- ever, the mean scattering of sound waves, for random orientation of the incident wave, is surely isotropic in azimuth. This is the situation developed in my lecture. af ales a eae oy i ; Ln Oey Tak ru vai 1 f i) ee A i ¥ . ‘ WDE ON NO anre VRC tt Thea h Th aT | erat irae 1 te FELINE LPT BS Tea ES ie \ { mS i . 14), th } ie VETO ate » id: Bor 3 hi Ward ay 4 i miisive Ube TAY eve tee at tee CTE i 7 i 1 i mit " : be ee SE 4 p ' i $ vi { uv! ("i ee # af vi De eAT yt i / ry Py *} , Aa Tek iy ay fi \j / lia ue ihe ph as ; telmdiideth i) } yt lau fi i" i ‘ F ; a ba i ' j i { “4 ne rity F ‘ y ate : 41 TPN Nag lt f if ; f i : if ' i ‘ } j i ‘y . > Ty Le i LECTURE 12 THERMAL MICROSTRUCTURE IN THE SEA AND ITS CONTRIBUTION TO SOUND LEVEL FLUCTUATIONS E.J. Skudrzyk Ordnance Research Laboratory The Pennsylvania State University University Park, Pennsylvania U.S.A. 12.1. THE TEMPERATURE STRUCTURE OF THE SEA Bodies of water such as the sea are acoustically inhomogeneous because of the dissolved substances, suspended particles, turbulent motion and water cur- rents, temperature gradients, and inherent microscopic temperature fluctuations. Temperature, which has the greatest effect on sound propagation, varies with daily and seasonal changes in the radiation from the sun. Variations in solar radiation cause temperature changes that take place over long distances and vary slowly with time. The turbulent motion of the water, on the other hand, generates microscopic temperature fluctuations from one point in the medium to another. The sea surface is coldest at midnight and warmest at noon, and these sur- face temperature variations penetrate deeply into the medium as Fig. 12.1 illustrates. The curves of Fig. 12.1 are interesting because they have been computed on the basis of some very reasonable assumptions (concerning the radiation from the sun, evaporation at the sea surface, and turbulent heat con- duction of the water). The unknown constants have been selected so that the curves coincide with a set of experimental curves measured at Key West, Florida. The only discrepancy occurs when the slopes become negative. These parts of the curves are not realized experimentally: the upper surface layers are heavier than the lower layers, and turbulent motion sets in. This surface-temperature instability generates strong turbulent motion in the sea, causing equalization of the temperature and generation of the so-called isothermal layer. The tem- perature gradients and long-scale temperature fluctuations lead to bending of the sound rays; they have been thoroughly investigated in recent years. Figure 12.2 shows the microscopic variations of the temperature for various depths, as recorded by Urick and Searfoss [1] with a resistance thermometer (the temperature fluctuates by a few thousandths up to a tenth or over a full degree). These readings exhibit a surprising space periodicity, as if the tem- perature distribution had been generated by a resonance phenomenon. In the. 199 200 Lecture 12 TEMPERATURE ———* 2 DEG FORENOON MIDNIGHT- EVENING EARLY MORNING ISOTHERMAL LAYER THERMOCLINE NONDIMENSIONALIZED DEPTH, kx Fig. 12.1. Computed daily variations of the mean temperature of the sea. literature on sound scattering half of this space wavelength is always identified with the diameter of the so-called temperature patches. An extended study (Fig. 12.3) shows that the patch radius is approximately equal to the depth at which the measurement was taken; the points of the "patch radius vs depth" lie as close to the line "patch radius equal to depth" as can be expected for sta- tistical measurements. This result is very strange and hard to understand, but DEPTH: 25FT DEPTH: I1OFT Fig. 12.2. Microthermal variations at various depths. a L DEPTH: 170 FT 40 YD E. J. Skudrzyk 201 20 PATCH DIAMETER (ft) Fig. 12.3. Patch diameter vs depth. PATCH DIAMETER = 2 x DEPTH (Urick —Searfoss data) Ke) 2 4 6 810 20 40 6080100 200 400 6001000 DEPTH (ft) there is consolation in the factthata similar result has been obtained for patches of turbulence. The classical mixing length, which is equivalent to the radii of the turbulent patches, has been found to be 0.4 times the distance from the wall. The classical theory of turbulence did not satisfactorily explain this strange relationship, and this is probably the main reason for the rejection of this theory in recent years. The measurements of the temperature structure of water in- dicate that the classical mixing length is not just a mathematical artifice; it has physical significance and can be determined experimentally. The next important step in the study of the temperature structure of water is to determine the average temperature deviation between two points as a func- tion of their distance. This has been determined by L.C. Pharo [2] (Ordnance Research Laboratory), who used the thermistor bar shown in Fig. 12.4 to meas- ure temperature fluctuations. This bar, which is equipped with thermistors at distances of 1, 2, 4, 8, 16, 32, 64, and 128 in., led to impressive results. The - temperature fluctuation increases very little with the spacing between the ther- mistors. A closer study reveals that the rms temperature fluctuation increases with the cube root of the spacing (Fig. 12.5). If, for instance, the fluctuation is 0.001° for a spacing of 10 cm, the rms temperature fluctuation increases to only 1° for a spacing of 100 km. Again, a law that is similar to a well-known law in the theory of homogeneous turbulence has been confirmed. The rms fluctuation Lecture 12 202 Fig. 12.4. Thermistor bar for measuring thermal microstructure. 104 KOLMOGOROV CASE ~ \06 oO oe o = o — qa 6 8 10 20 40 60 80100 200 400 600 (000 THERMISTOR SPACING (in.) Fig. 12.5. Horizontal temperature distributions as measured in the sea. E. J. Skudrzyk 203 of the turbulent velocities is found to vary in exactly the same manner, and is explained by the Kolmogorov equilibrium law [3,5] for the spectral space dis- tribution of the turbulent velocity fluctuations. This law is of the form indyakie 8 (1) where K is a constant and x is the space wave number. Such a power spectrum leads to the cube-root distance law, <(As)?> is equal to constant times p”, where p is the distance; and, vice versa, a cube-root distance law leads to such a power spectrum. The Kolmogorov equilibrium law then turns out to be a general law of physics that applies not only to turbulence, but to many different phenomena, This law applies whenever the following sequence takes place: energy is introduced into a fluid at a constant rate, is redistributed until a state of equilibrium is attained, and is eventually dissipated by friction or heat conduction. The only other as- sumption necessary is that the fluid be infinitely extended. Dimensional con- sideration then leads directly to this law in the following manner: the energy Dp introduced per unit mass per unit time has the dimensions Dyas (2) where the expression derivable from the kinetic energy (mv”) has been used to arrive at the dimensions of energy. The magnitude of interest is the power spectrum E(x) of the phenomenon to be investigated. The power spectrum has the dimensions of energy per unit mass per unit space wave number, or 2 2 3 BGS) HRS UE ee UI oe (3) where x = 27/\sp (Asp is the space wavelength and has the dimension/~*). The power spectrum must be a function of the parameters that are available for the de- scription of the phenomenon. Since the fluid has been assumed to be infinitely extended, the only available parameters are Do andx. Hence, E(x) must be a func- tion of D, and x: E(x) = f(Do, k) (4) which, in the simplest case, when written as a power product, is of the following form: E(k) = DOK" (5) Since the dimension of the right hand sides of Eq. (5) and Eq. (3) must be the same, the following relation must hold for m and n: 3 _ pmyn 12% jon E(x) =“g = Dox" = (6) When we equate the exponents 3=2m-—n 2=3m (7) 204 Lecture 12 Hence, amok poo 3 3 (8) and E(k)=D¢2x- 73 (9) which is the well known Kolmogorov law. Because of the generality of the as- sumption, it is not surprising that this law also describes the temperature fluc- tuations in the sea. (SSeS MEASUREMENTS WHEN SEA WAS PART HOMOGENEOUS 6) iG 10 100 1000 10000 PATCH DIAMETER (in.) Fig. 12.6. Establishment of the equilibrium law for the range of small patches. E. J. Skudrzyk 205 The simple form of the Kolmogorov law applies for the equilibrium range of the phenomenon, which, by definition, is unaffected by the mechanism of the redistribution and the energy dissipation [4]. If the fluid is not infinitely ex- tended—if, for instance, the receiver is at a finite distance from the water surface—an additional parameter is available to describe the phenomenon. In altering the Kolmogorov law for this case, let us be guided by the experimental results. 10°9 25 FTX DepTH -10 10 9 FT 170 FT (B) 120 FT 170 FT (A) iol! = Co, Ss oO iy = la 2 10 's tad LP) oS oa = 5 COMPUTED FOR A KOLMOGOROV-TYPE S193 POWER LAW ASSUMED AS 2 FOR A 50 FT SPECTRUM CUT OFF AT THE LOWER WAVE -NUMBER END 10° “0,001 001 Ol l 10 100 PATCH DIAMETER X + Fig. 12.7. Curves of Fig. 12.6 represented to a normalized scale. 206 Lecture 12 Figure 12.6 shows an extension of the rms temperature fluctuation meas- urements for long distances. As the distance is increased, the slope increases above the value given by the one-third power law. However, when the distance between the two points becomes equal to the depth of the measurements, the curves become practically horizontal. It is relatively easy to show that this dis- continuity in the slope of the measured curve is due to a similar discontinuity in the slope of the power-spectrum frequency curve (or that it is even due to a cutoff of the power-spectrum) at a wavelength equal to one-fourth the depth of the measurement. Figure 12.7 shows a curve that is computed on the assumption of a Kolmogorov-type power spectrum and cutoff. This curve is similar to the experimental curves shown in the same figure. The discontinuity in the slope of the power spectrum also can be found directly from a Fourier analysis of the temperature fluctuations (Fig. 12.8), or from a Fourier analysis of the cor- relation function of the temperature fluctuations (Fig. 12.9). The results shown in Fig. 12.8 are of an orientative nature only, and the measurements are still affected by the time constants of the recording equipment. The frequency spec- trum shown in Fig. 12.9 is practically constant up to a wave number equal to the depth, and decreases with increasing frequency. Figure 12.10 shows similar results obtained for the turbulent velocity fluctuations in a boundary layer. The last result makes it possible to prove that the approximate constancy of the thermal patch diameters in all the temperature recordings (see, for in- stance, Fig. 12.2) is not due to a predominant spectral space component of the temperature fluctuation, but is due to a cutoff of the spectral distribution. For instance, let us consider a Fourier distribution with slowly varying amplitudes A(t) and slowly varying phase angles w(t). (The introduction of A(t) and y(t) elimi- 22:1073¢ THEORETICAL CURVE 22:10°4 EFFECT OF TIME CONSTANT OF THERMISTOR e |28-IN SPACING ° °,, > © 16 - IN. SPACING +++ °+ 9 eh + 64-IN. SPACING 22-1075 ++ Or % \e ek ° TEMPERATURE FLUCTUATION (deg C/unit wave -number interval) Fig. 12.8. Space spectrum of the temperature fluctuations. 22-1076 w TIME CONSTANT~6 * OF FILTERING + CONDENSER 760 76 7.6 076 0.076 SPACE-WAVE LENGTH (cm) E. J. Skudrzyk 207 10 (ce) EW=afes cos bs cos(ks)ds (0) e) i l l 20| + (beke aa for a=0.20 and b=0.27 TOTAL SQUARED THERMAL DEVIATION (per cent) Ol | 10 100 WAVELENGTH (yd) Fig. 12.9. Power spectrum obtained from an analysis of the correlation function R(p) = e 2-295 0,27 which represents a good fit to the experimental results [1]. nates the necessity to perform the Fourier integration over an infinite interval of time.) The time function, then, is given by fae coslwt + U(]da (10) A maximum is attained whenever ot + w(t) =0 for mostof the spectral components of the distribution. In the vicinity of such a maximum, the above integral may be crudely approximated by the following expression: 229 i i f Acosat dw = Aes, eet = Ado Sin x (11) 0 @ot x It has been assumed that the spectrum is of constant amplitude 4, and that it is cut off at the frequency wo. The time function is thus of the form (sinx)/x. The amplitude fluctuates, and the period of the fluctuation is equal to the cutoff period. Actually, the spectrum is not constant, but is of the Kolmogorov type. It can be shown that for such a spectrum the fluctuations are still larger. The above conclusions can be easily illustrated by experiments in which the space coordinate is replaced by the time. For instance, curves very similar 208 Lecture 12 107-2 M Harrison \ (Flow Noise) \ \ 10-3 T ay Water Tunnel ORL 1075 ENERGY SPECTRUM FUNCTION, F(n), sec Fig. 12.10. Power spectrum of boundary layer turbulence. 1077 io 8 10 10° 10° 10 10 FREQUENCY, n, cps to the temperature recordings are obtained when white noise is passed through a high-pass or low-pass filter and the filtered output is observed with an oscil- loscope. The cutoff frequency can always be identified by the predominant peri- odicity of the output, which has a period equal to the cutoff period of the filter. Changing the cutoff frequency of the filter changes the periodicity of the output. Another very similar phenomenon is observed in the detection of sound by an early type of condenser microphone. The transients of the sound generate decaying vibrations of a period equal to that of the cutoff period of the micro- phone. The ear, which integrates over only a short interval of time, perceives these transients as a hiss at the frequency of the microphone. In a long-time Fourier analysis, the fluctuations cancel, but they always appear in a short-time analysis of the noise, such as that performed by the human ear. This fact is illustrated by Fig. 12.11 in which the left half of the curve is in antiphase to the right half of the curve. The contributions of the two halves of the curve cancel in the Fourier integral. If, however, the Fourier in- tegration is limited to the right or left half of the curve, Fourier analysis leads to a predominant component of a period approximately equal to the period of the fluctuation of the curve. The generation of the cutoff in the power spectrum at a wavelength equal to about four times the depth of the measurement still needs explanation. Un- E. J. Skudrzyk 209 . Fig. 12.11. Fluctuations in which the left half are in antiphase to the right half. fortunately, no satisfactory explanation has yet been found, but a plausible explanation can be derived with the aid of a statistical method [6] that was introduced by Lande in 1913. This method, which represents an expansion of the procedures used in thermodynamics today, analyzes the physical system by counting the number of its degrees of freedom and by attributing a certain energy to each of them. The degrees of freedom are identified with the number of pa- rameters that are required to describe the system, such as the number of the Fourier coefficients that are finite. This method has been very successful in recent years [7], although it does not seem to be fully understood at present. The temperature fluctuation within the finite layer of water between the surface and the point of measurement can be represented by a Fourier series. If isotropy is assumed in this layer, no consideration need be given to what happens at greater depth, and the layer canbe assumed to be repeated periodically. Because of the continuity of the temperature distribution, the lower boundary has to be a plane of symmetry in this periodic pattern of layers, and the longest wave- length required to represent the temperature pattern is therefore equal to four times the depth. Since the lower boundary of the layer is not plane but distorted and fuzzy, the phenomenon is not strictly represented by a Fourier series but by a Fourier integral. However, the envelope of the spectrum may still be con- sidered as approximately that of the series, with the low frequencies also filled in (because of the nonperiodicity of the actual temperature pattern). 12.2. THE CHARACTERISTICS OF THE TEMPERATURE STRUCTURE OF THE SEA The static thermal conductivity of water is extremely small. Temperature patches would have a lifetime of many months if they were not split up and de- formed by turbulent motion. There is, therefore, little doubt that these patches are originally generated by turbulent motion and represent "frozen turbulence." The energy that is fed into the water by the radiation of the sun and by the wind acting on the sea surface seems to be predominantly used for the generation of very large turbulence patches and temperature patches (see Fig. 12.6). The large patches eventually split up into very small patches; thus, the turbulent and the thermal energies are passed down by a kind of cascade process to the range of the small and very small patches (or space wave numbers). The in- tensity of the large-diameter patches depends on the weather and on the depth 210 Lecture 12 of the measurement, and is considerably greater than the intensity predicted by the Kolmogorov equilibrium law (see Fig. 12.6). However, as the patch size becomes smaller, most of the fluctuations caused by the weather and by the daily variations of the temperature seem to average out, and a stable Kolmogorov-type space spectrum is generated. The slope of the curves in Fig. 12.5, then, is exactly one third. When the space wavelength becomes very small, the effects of viscosity and heat conduction predominate, and the tem- perature fluctuation eventually decreases inversely to the seventh power of the space wavelength [4]. This range does not appear in Fig. 12.5. The space spectrum of the temperature fluctuations of the sea can be divided into three different regions; (1) the long wave number range, (2) the equilibrium Kolmogorov range, and (3) the dissipation range. The long wave number range, which depends greatly on the depth of the measurement, and which also seems to depend greatly on the weather and its history, as will be discussed in the next section, has practically no effect on sound scattering or the fluctuations of the transmitted signal. These are predominantly determined by the spectral com- ponents of the temperature pattern that have a wavelength A,, equal to, or greater than, half the sound wavelength up to wavelengths somewhat above that given by r=kR’, where r is the range, and R ~X,,/4 represents the radii of the tem- perature patches. For the sound frequencies of practical interest, the spectral components of the temperature structure that affect sound propagation are always within the Kolmogorov equilibrium range. The spectral distribution curve of the temperature fluctuations in water, as far as they affect sound propagation, can be assumed to be independent of the weather or the external conditions of the Kolmogorov type, E(k)= Kx- 3, This assumption leads to a considerable simplification in the theories of sound scat- tering and of the fluctuations of the transmitted signal. All that needs to be de- termined in the Kolmogorov law is the constant K as a function of the depth and of the variations in the weather. This can be done by measuring the rms temperature fluctuation between two points at a constant distance from one another. The results obtained in the past by acoustic measurements seem to indicate that the value of this constant decreases with depth, but depends only slightly on the weather. The constant K can be expressed as a function of the mean-square deviation of the sound velocity. If the power spectrum is constant up to a space wave number x), and if it obeys a simple power law for the higher space wave numbers, E(k)=Kx-™ KS Ko (12) E(k)=Kko™ K2 Ko the mean-square value of the velocity fluctuations then becomes KO © ha : a? =f E(x) de = Kea" + [Kee dk =—@ Kd (13) The constant K, therefore, is given by K=Ma1 po q? (14) E. J. Skudrzyk 211 Actually, m and XK are not constant, but increase toward the long wave number end. A more accurate determination of K can be obtained for the Kolmogorov range by measuring the rms temperature difference between two points sepa- rated by a distance that is of the same magnitude as the diameter of the acous- tically active thermal patches (about 10 ft apart; see next section). It can be shown [8] that the equation [ox +p) - e(x)]? =4 f B() (1 - sina) dk =BK x? (15) depends predominantly upon the value of E(x) for xp =1, and that the constant B is equal to Oe in the range xp ¥1, even if the Kolmogorov law is only an approximation. 12.3. THE SCATTERED PRESSURE AND SCATTERED INTENSITY 12.3.1. The Rayleigh Integral The classical as well as the modern theories of scattering are all based on the Rayleigh integral [9]. This integral represents the solution of the wave equa- tion for the case in which the properties of the medium deviate slightly from their average values. This solution shows that the density changes caused by the natural temperature fluctuations have a negligible effect on sound propa- gation in comparison to that of the changes in sound velocity. But if the local variations of the density are neglected, the derivation of the wave equation is the same as that for a homogeneous medium except that the sound velocity now is locally variable. Therefore, for periodic vibrations, the wave equation is V*p+k*p=0 (16) where 9 K2 -2(1 -2Ac avd Sp G@ = Da) In Eq. (16), c= co + Ac, the magnitude cy = < c > represents the space-average value of the sound velocity, kg =@/cp is the wave number of the undisturbed medium, and a= Ac/eo (17) is the relative deviation of the sound velocity from the space-average value. The variable part of the term that contains the sound velocity may then be trans- ferred to the right-hand side, thus: Vp + kop = 2kaap (18) Since only a small fraction of the incident energy is scattered per unit volume of the scatterer, the right-hand side is small and the sound pressure on the right-hand side may be replaced by the sound pressure, p;, of the incident wave. The solution of the resulting equation is well known; it is given by P=P;i+DPsc (19) where the scattered pressure 212 Lecture 12 fe eTkor Psc=97 J 2Pi Sr (20) is represented by the Rayleigh integral [9] taken over the total scattering volume and the distance r is given by r= (x- €)?+(y - €)? +(2-&) (21) No assumptions other than Ac/co <1 have been required in the derivation of this formula. To simplify the notation, ko has been replaced by k, where k represents the average wave number in the inhomogeneous medium. As is standard practice in acoustics, the solutions here and in the following pages are represented in complex forms. The actual solution is given by the real part of the complex solutions. Physically, the Rayleigh integral denotes the sound pressure radiated by a source distribution that is excited by the incident sound. Every elementary vol- ume of the fluid turns into a sound generator that, at the expense of the energy of the incident sound, radiates (scatters) sound in all the different directions. The simplest and most efficient way to study scattering problems is to con- sider a parallel beam of sound p,; =poe~*? propagated in the direction of the positive £ axis. The scattering volume may be assumed to be small in compari- son to its distance, ro, from the receiver and to be centered at (€ 7, €)=0. Let the point of observation have the coordinates x, y, andz. The scattered pressure then is given by the Rayleigh integral pse (x,y, 2)= =F fa 1, 6) 5 pve" Jak dn dl (22) Tr where a = Ac/cy is the relative change in sound velocity and r [see Eq. (21)] is the length of the radius vector. It is standard practice to develop r, the exponent, into a Taylor series: xE yn 26 € 477+? Gene Ge ee ea Le ae 0 Se | (28 =o Rear + Tp + /..=% —(a&+ Bn +yl)+ Ore + (23) In this equation ro is the distance of the receiver from the center of the scatter and a=x/ro, B=y/ro, and y=2z/rpg denote the direction cosines of the scattered sound. The Rayleigh integral then simplifies to Psc (x, y, z) = kp (2 - a- 7B - &y - 1)] dédnd€ (24) 27 3 To In the denominator, r has been replaced by rp on the assumption that the dimen- sions of the scatterers are small in comparison to the distance of the scatterer from the sound receiver. For forward scattering (@=f8=0, y=1, and @)=0), the scattered pressure becomes k2 —jkto a2 . ; Psc (0) a 2.a(p) p2dp = tt ep (25) E. J. Skudrzyk 213 e wher 2x2pyaR3 3 Si is a measure of the strength of the scatterer; the magnitude s is equal to the amplitude of the scattered pressure at unit distance from the scatterer. Thus, the pressure scattered in the forward direction becomes proportional to the product ar, where a is the average deviation of the sound velocity from its mean value over the volume ; and ; is the volume of the scatterer. Polar coordinates p, 9, and ¢ have been introduced to replace €, 7, and ¢. 12.3.2. Spherical Scatterers A great deal of information can be obtained by considering the simple case of a spherical scatterer and assuming that the sound velocity is a function of the distance from the center of the scatterer only. The angular integration can be easily performed as follows. The quantities a, B, and y- 1can be considered components of a vector A of magnitude A=l[a7+ B? + - 1)2]% =(2(0- yl” = (2(1-cos Oo)” =2 sin 22 (26) 4 is the angle between the direction of the incident sound (that of the z or ¢ axis) and that of the scattered sound (@)= 0 for forward scattering). The magnitude 4 and the direction (a, 8, and y-1) of the vector A depend upon the scattering angle only. In the integration over the scatterer, A is constant; therefore, the vector A may be assumed to be the axis of a system of polar coordinates p, 0, and ¢. The exponent in the integrand in Eq. (24) can then be written pAcos 6; and the integral becomes independent of ¢: -jkr 2 ith 4 = kpoe ieren0 : k2ppetkto 2 Deg =—————_ a(p)el*4°C°S"a(-cos 6) p2dp Ae eS a(p) sin(I'p)pdp to h 0 Les To (27) where I= 2k sin(@)/2). The Rayleigh integral now becomes solvable for several different velocity distributions. In the classical theory of scattering, the dimensions of the scatterers are small compared to the wavelength of the radiation and the distance from the scatterer, ry. The phase change of the incident pressure, p;, and the scattered pressure, p.-, over the volume of the scatterer, 7 = 47R*/3 (where R is the radius of a sphere that has the same volume as the scatterer), may then be neglected; the scattered pressure Boke e7/K0 _ 87°Rpo R .-~ikn PE Pe ae Sree oe v (28) becomes independent of the scattering angle and is proportional to the square of the ratio of the diameter tothe wavelength. Particles that are small compared to the wavelength of the radiation are, therefore, very inefficient scatterers. If the scatterer is a finite sphere of constant sound velocity, the integral for scattered pressure in Eq. (27) simplifies to =, R as : cl Spc SETI i sin (Up) pdp Ss oig nS seens R°T'r0 0 uo ¢ (29) 214 Lecture 12 where €=IR = 2kRsin(@)/2). The scattered pressure has decreased tohalf its max- imum value when ¢€= 2.50 rad. The corresponding scattering angle is given by Pos) Xv ) 0 (29 sos —— = OVS 30 i nEOMNRER 2R (30) Outside this region, where sin ¢ « cos ¢, the scattered pressure becomes ps —jkr, yr Psc = a a (31) For small values of ¢, that is, for scattering in the forward direction or for low frequencies, the Taylor development leads to the classical solution [Eq. (28)]. For a large scatterer, the scattered pressure fluctuates rapidly with changing scattering angle, and the envelope of these fluctuations decreases inversely proportional to the square of the sine of half of the scattering angle and to the square of the frequency. The phase of the scattered pressure is given by that of the incident wave at the center of the scatterer and the distance of the point of observation from the center; therefore, it corresponds to the distance the sound has actually traveled. However, this result applies only if the scatterer is very small in comparison to the distance from the scatterer, so that the higher-order terms in the Rayleigh integral can be neglected. It is also interesting to study the effect of a continuous transition of the sound velocity from the undisturbed medium to the center of the scattering patch. Four cases of a gradual velocity transition are easily soluble [10,11]. They are represented in Table 12.1 as cases 3 to 6: ag(l1—r/R)? for rR (32) ao Ore ayugetevereeet ene ———— ae) [1 + (r/R)7I? icons tokcrsvele shaw a@ysenen Figure 12.12 shows a graphical comparison of the scattered pressure for the cases represented in Table 12.1. The ordinate represents the scattered pres- sure; the abscissa, the quantity [r, whichis twice the product of the undisturbed- medium wave number with the effective radius R of the scatterer, as defined by Eqs. (82) and the sine of half the scattering angle. Forward scattering is, thus, described by points on the vertical axis, and backward scattering is described by points that, proportionally, are more to the right as the wave number and the radius of the scatterer become greater. Since the same scat- tering strength has been assumed [see Eq. (25)], forward scattering is the same in every case. For a given scattering power or a given volume of scatterers, the classical scatterer is by far the most effective. The scattered pressure is independent of the angle and has the maximum value possible. If the scatterer E. J. Skudrzyk Relative deviation of sound velocity, a ao, RKA ao, rSR aoe ao(1— r/R)°; rSR 0; r>R TABLE 12:1 Scattered pressure referred to classical scatterer of sames, D(8o) sin! R-TRcosTR (FR)* 1 a+T?R?) Remarks Classical scatterer Spherical scatterer of constant sound velocity Exponential increase of sound velocity Parabolic velocity increase 215 ao [1 + (r/R)?]? eT (r/R)? Gaussian increase a ° of sound velocity is large compared to the wavelength of the radiation, the scattered pressure decreases at least as ([R)~” (see Table 12.1). It fluctuates above and below this value for a sphere of constant sound velocity and approaches this value asymp- totically if the change in sound velocity is exponential. The pressure scattered backwards by a large scatterer decreases at least inversely proportional to the square of the frequency and the square of the radius of the scatterer. Sharper transitions than the exponential, such as those of cases 4 and 5 in Table 12.1, lead to considerably less backscattering. Scatterers that exhibit a Gaussian ve- locity distribution produce a particularly small amount of backscattering. Forward and backward scattering, then, are almost completely independent phenomena. Forward scattering, as will be shown later, essentially describes the phase change of the wave caused by the scatterer. This phase change is pro- portional to the average change of the sound velocity over the scatterer, and consequently it does not depend upon whether the change is abrupt or continuous. Thus, all scatterers that exhibit the same average change of sound velocity over their volume (i.e., they have the same scattering strength) generate the same amount of forward scattering. The scattered pressure reaches a maximum in the forward direction and decreases with increasing scattering angle. Backward scattering, on the other hand, is essentially a reflection phenomenon; therefore, it depends greatly on the details of the variation of the sound velocity across the scattering patch. The results given above can be generalized to fit the case of a fluid contain- ing a large number of scatterers. Because of the small deviation of the sound velocity from the average value, there is equal probability that this deviation may be either plus or minus; therefore, the energies add, and the intensity scattered becomes directly proportional to the average ofthe intensity scattered 216 Lecture 12 = CONSTANT < % CLASSICAL SCATTERER SPHERE \e2m Yau Ae fo) ° ° ¢ a 8 a ¢ 8 + + 7 y T T ' ' 1 1 (QP) HLONSYLS ONINSLLVIS SWVS JO ¥3Y4311V9S TWWOISSV1D O1 G3YY3SISY S3YNSS3Y¥d Gy¥311V9S 20 =} 16 Tr Fig. 12.12. Scattered pressure as a function of scattering angle and frequency for five cases. E. J. Skudrzyk 217 by a single scatterer and the number of scatterers. For constant density of the scatterers, the scattered intensity is proportional to the total scattering vol- ume. A further elaboration of this procedure, however, is of little practical value since the true temperature field is of a statistical nature and cannot be described by a collection of individual scatterers. 12.3.3. Scattering Described by the Correlation Function If the temperature field is not made up of simple temperature patches, or if a detailed description of the scattering inhomogeneities is not available, the scattering properties of the fluid can be described by the correlation function R(p) or the space power spectrum E(x) of the sound velocity fluctuations, x being the Fourier space wave number. The Rayleigh integral can be transformed into a form based on the correlation function by multiplying p,. by its conjugate com- ples value, p.., and taking the time EXISTE Cc If the variables are denoted by ¢’, 7’, and ¢’ in the first integral and by &", n’, and ¢” in the second, the product of the see can be written as ri>-eom ae [ [oe P:.| = bacPD Ga ees x etKl(E' "ae (=n B+ (E' - 8) (y-DI gé"an" do dé'dn' do’ (33) where the integral sign denotes triple integrations over the primed and double- primed coordinates, and L is the linear extension of the scattering medium in the three coordinate directions. If the medium is statistically homogeneous, the time average al(E'n'L') al (En £") = a?R(p) (34) is a function of the distance p ofthe two points é'7'¢' and &"n"¢" only. This time average is then assumed to be the same as the space average (Ergodic hy- pothesis). The time average a’a” has therefore been replaced by the space average in the above integral. The magnitude R(p) is called the normalized correlation function. If, the two points are coincident, p=0, — , and R(0)=1. If the points €'7'¢' and €"n"¢" are far away, a’ and a” can be assumed to be independent of one another; then = = 0 because of a well- known theorem of statistics. The above ets can then be written as follows: (pid>= ce Lars La Bcf I R71, 0) ike +6n+¥-) 1 géandtdt'dn'dl' (35) where é'- €", 7'~7", and ¢'-¢" have been replaced by €, 7, and ¢. The €', 7, ¢’ integration leads to a factor oe to the volume ; of the scattering region. The é, n, ¢ integration is performed in exactly the same way as in Eq. (27). The re- sult is 2 k*po . A) £20, ,<2> | Rip)sin (Cp) pdp (36) L 218 Lecture 12 The last integral is very similar to that which applies to the scattered pressure. The deviation, a, of the sound velocity from the mean value has been replaced by R(p). The number of scatterers is proportional to the volume T of the scattering media, which therefore appears as factors in front of the integral. The results obtained for a number of interesting cases are summarized in Table 12.II] and plotted as curves in Fig. 12.13. They will be discussed later and compared with the corresponding results for the Kolmogorov case. 12.3.4. Scattering Described by the Power Spectrum of the Sound Velocity Fluctuations Frequently the correlation function is unknown or it is too complex to be useful in integrals. It is then expedient to describe the fluctuations of the sound velocity of the medium by its Fourier space spectrum. The relation between the correlation function and the power spectrum ¢4(k,,k2,«3) of the velocity fluc- tuations is given by KFS I2(EnneanGe) = 10 (ki, Ko, K3) loses +k2&2 +K3&3) devisees (37) 0 If the fluctuations are isotropic, $(k:1,k2,x3)= (kx), Where x is the magnitude of the wave number, and & (k1, Kz, K3) dky dk2 dk3 = $(k) 27K7*dk sin @ dO = E (x) dk sin 0 dé (38) = where E(k) dk = ®(k)47K7dk (k 20). The exponent in the integral in Eq. (37) can be written as x-p =xpcos@, and the angular integration yields R(p)= [ eqosineds (39) 0 (kp) If this value is introduced into the scattering integral in Eq. (36), L <|p2<)> " ao i; J E (w) sin (kp) sin (Ip) dpdk (40) TT lb Lo Ik and if Lis very large (L + ~), the results becomes [11] 4p()__k* El2ksin@,/2)l k = aE STONOUELE 41 i EG ey | ER Pee a Thus, the scattered intensity becomes proportional to the spectral intensity E(x) of the temperature field for a wave number « = 2k sin(@)/2). A similar result was obtained in the analysis of X-ray scattering over forty years ago. The structure factor was found to be equal to the corresponding Fourier coefficient of the atomic structure. For back scattering, @)=7 andx=2k. The patch diameter may be crudely identified with half the space wavelength of the temperature fluctuations, i.e., 2R =\,,/2=7/k (where k=7/2R); backscattering is thus caused by patches of a diameter 2R =e =e (42) E. J. Skudrzyk 219 TABLE 12.11 i i < [pee limes Correlation function R (p) Pscl 7 _ kT gts] or power spectrum E (k) |pol Qn The above factor ] cr Case —1/R R(p)=e 8nR*/[1 + (CR)7]? 2 | R(p)= en (t/R)? 7/2 R3 - UR/2)? 3 | R@M=l+@/R77? TRie-TR AC af 3 4 | R@=G-1/R);rSR p= Be epaiP4 2 wc Pr] (rR) [TR R(p)=0;r>R 1 2 _ a (m— 1) —m by E(k) ge (K/Ko) Gas) KB 2 for K= ksin(9/2) > Ko pat TK , 3 ey k 2r 6 | e«)=Kx7 2 7 [2 sin(O9/2)) °° As the angle between the direction of incident sound and the direction of scat- tering becomes smaller, the scattered intensity is determined by larger patch sizes. The spectral intensity of the thermal fluctuations increases with decreasing k; scattering, therefore, increases toward the direction of the traveling wave. Scattering in the forward direction is described by the very large patches; the first-order approximation, Eq. (20), that was obtained by retaining only the linear powers in the Rayleigh integral, then breaks down. A better approximation (see Section 12.4) shows that the pressure scattered by very large patches is 90° out of phase with the transmitted sound and affects the phase rather than the amplitude of the signal. The scattered pressure, then, is no longer coherent with the incident sound; the scattering integral degenerates to a mathematical correction that has no physical significance, and its square is no longer a meas- ure of the divergence of the energy. The scattering integral p.. primarily de- scribes the change in phase because of the variation of the sound velocity in the medium. If the power spectrum of the sound velocity fluctuations is of a Kolmogorov type, Eq. (41) leads to _ rk*K 2k sin(Oo/2)~”? _ 1K 4 ¥5 (963 =1/, oe TORE [ak sin (6,/DI2 SoH (2 sin (0o/2)] (43) Scattering, then, increases with the cube root of the frequency. For forward scattering, 0, =0, and the above solution breaks down because of the assumption L + ~ in the evaluation of theintegralin Eq. (40). If the p integration is performed for finite L, the solution becomes (coke (ioe) BniGeein yo itn au BS Seo EM9) SENS UNS 44 “yoo mre | Tk ; K-T K+T ‘ ) 220 Lecture 12 O;r>R (1-(r7R)?); r SR -r/R Fig. 12.13. A comparison of the scattered intensities for cases of practical interest. J E. J. Skudrzyk 221 and the integral approaches a finite limit. It is possible to derive approximate expressions for this limiting value. However, there is not much point in doing so, since the computation would be equivalent to a computation of the phase change of the signal because of its different velocity in the medium. In the Kolmogorov case, m= fy and the resulting solution is represented in the last line of Table 12.11; the Kolmogorov equivalent for the patch radius R is the depth h of the measurement, since the depth is the only dimensional param - eter that is available and x) =7/2h. In the curve for the Kolmogorov case in Fig. 12.13, therefore, R has to be interpreted as 4A. Figure 12.13 compares the scattered intensities for the case of practical in- terest. The most frequently usedcorrelation functionis the exponential e~/* since integrals based on this function can usually be evaluated. Also, the exponential correlation function seems to lead to good agreement with the experimental re- sults in a great number of practical cases. Figure 12.13 shows that the expo- nential function generates about the same amount of scattering as the function R(p)=1-(p/R)?, r” IRL sat - I ie sin 22P- R(t) dndéd€, dé. (61) a Hee ples v 2 tf 192 For a parallel incident beam of sound, and for a Gaussian correlation function 2a2seq eR? = SPs KA ty? + el /n? (62) I, = V7 k? RL and las psa > kOR® tan7! = (63) 226 Lecture 12 100 10 | es «< SS 0. kr N Ol 0.0015; | ile) 100 L/k?R? Fig. 12.16, Scattering as a function of frequency [51]. With the abbreviation 4L D ~kR? the mean-square scattered pressure becomes 2 2 ie . =F - b)= fF k? RL =f tan ‘D) (64) This solution is represented in Fig. 12.16. For large values of range, this so- lution passes over in the wave-theory expression for interference scattering. 12.4.3. Continuous Patch Distribution In the general cases, the patches of inhomogeneity are not adequately rep- resented by a simple Gaussian correlation function. The two experimental Gaussian terms yield a poor representation of the experimental results. It then becomes expedient to replace the correlation function by the power spectrum E. J. Skudrzyk 227 of the velocity fluctuations. The relation between the correlation function and the power spectrum is +0 +0 +0 R@=f il b(k) eltka E42 7443 Hence (65) bal?) -0 -0O The scattering integrals have been represented in cylindrical coordinates. It is expedient, therefore, to express the correlation function in cylindrical co- ordinates too as 2 2 277 cos ji 1 1 R(r) = [fe ffs) d(x) e” HIE Bk dk, (66) where @ is the angle between the p vector and the projection of the wave-number vector on a plane perpendicular to the & axis and G . k3=k cos@ Ko =k’ sin®@ Ki =K1 2 kK? = «3 +3 Ke = Ke + K? (67) The 6 integration can then be performed: R(p) = 2 ff b(k) cos(ky)K'd'dky 27]p (k’p) (68) where the lower limit of integration of x; =- ~ has been replaced by zero, and correspondingly, the exponential by the cosine. The integral 1, [Eq. (61)] becomes L L foo) fo) 2 boxe |) f J if $(k) cos (k,é)K'dk' dk, (2 sin = 2 i sf Jol p)p dn)aé ae, (69) where g= 5, =§ and aj = k/(é, - €2) and a3 = k[(2L =6 - €) The p integral parenthesis is known [10,11]. Its value is cos (x'?/2a2,). Hence 2 Lol 2 fo ns Me Sf J, i f (k) cos (k1&) kK dk'dk; cos ae dé, dé, (70) The value of these integrals depends greatly on the small-wave-number power spectrum of the fluctuations of the sound velocity where the Kolmogorov law no longer applies. For a square law as a first approximation rather than a of power law, and on the assumption that the spectrum is zero at wave numbers Kko E(k) = (71) 0 for kK xo and ko 2 2 MPS ARO ee (73) The coefficient of variation vy, is thus proportional to the root of the range and independent of the frequency. The L-range dependence seems to be certain, no matter what power has been assumed in the power spectrum; the frequency dependence, however, in only approximate. A still closer approximation to the Kolmogorov law (assuming m= 2 in the integrand so that integration becomes possible and m=, in the factor in front of the integral) leads to the result that scattering is proportional to the cube root of the frequency which is in good agreement with the experimental result. 12.5. EXPERIMENTAL RESULTS 12.5.1. Standard Deviation of the Transmitted Signal The fluctuations of the transmitted signal are usually described by their standard deviation and by their distribution law. The standard deviation is de- fined as the ratio of the square root of the mean-square deviation from the mean value and the mean value of the pressure me 2,¥2 y 1 Vasoe <@ = Po)" >“ _ a = a | 40 30 60-KC DIRECT SIGNAL © =SHALLOW DEPTH (50 ft) =DEEP DEPTH (100 to I50 ft) RELATIVE STANDARD DEVIATION (per cent) ie) 200 400 600 800 1000 1200 1400 1600 RANGE (yd) (a) 50 FOCUSING RANGE ——*| 25-KC DIRECT SIGNAL © = SHALLOW DEPTH (50 ft) x = DEEP DEPTH (I00 to 150 ft) 40 30 RELATIVE STANDARD DEVIATION (per cent) (0) 200 400 600 800 1000 1200 1400 1600 RANGE (yd) (b) Fig. 12.19, Direct-signal fluctuations measured in one day in July; (a) at 60 kc, (b) at 25 kc. As can be seen, the variability of the surface reflection is relatively high, 52% at short distances, but tends to decrease somewhat with increasing range. The variability of the direct transmission increases with distance, until at long ranges the same variability may be expected for the two paths. The slight de- crease in variability of the surface-reflected signal may be attributed to the fact that the sea surface becomes more like a perfect mirror and less like a E. J. Skudrzyk 231 diffuse scatterer within the small grazing angles existing at the longer ranges. At long ranges, where the signal is specularly reflected, the fluctuations in both the direct and the reflected signal have the same causes; at short ranges, the diffuse reflection from the surface is an additional and more important source of variability. Figure 12.18 shows two plots of the direct-signal fluctuations for one day. The solid lines represent the solution that would be computed if a Gaussian cor- relation function were assumed. By assuming a suitable value of the correlation distance R and of the rms fluctuation of the temperature, lines can be drawn that pass through the measured points with reasonable accuracy. To obtain a better fit for the low values of range, the correlation function would have to be assumed to consist of two exponential terms. Figure 12.19 shows the results of measurements made in July, when measurements of the temperature micro- structure were made simultaneously. The results of the measurements make it possible to test the prediction of Gaussian correlation functions and the Kolmogorov theory. The natural way to deal with scattering is to assume a continuous distribu- tion of patch sizes from the beginning, such as is given by the Kolmogorov law. This theory leads to considerably better agreement with the experimental results than the procedures based on the experimental or Gaussian correlation function. The values predicted on the basis of this theory are of the right mag- nitude, and the frequency and range variations are reproduced in a better manner than with the Gaussian correlation-function theory. Future measurements will, therefore, have tobe based exclusively on a Kolmogorov-type power spectrum of the sound velocity fluctuations. REFERENCES 1. R. J. Urick and C.W. Searfoss, "The Microthermal Structure of the Ocean Near Key West, Florida,” Part I—Description, Naval Research Laboratory Report No. S-3392 (December 7, 1948); Part II—Analy- sis, Naval Research Laboratory Report No. S-3444 (April 12, 1949). 2, D.C. Whitmarsh, E. J. Skudrzyk, and R. J. Urick, "Forward Scattering of Sound in the Sea and Its Cor- relation with the Temperature Microstructure,” J. Acoust. Soc. Am., Vol. 29, 1124-1143 (1957). 3, A.N. Kolmogorov, "Local Turbulence Structure in an Incompressible Liquid for Very Large Reynolds Numbers,” Doklady Akad. Nauk SSSR, Vol. 30, 299-303 (1941). 4, W. Heisenberg, "Zur Statistischen Theorie der Turbulenz," Z.Tech. Phys., Vol. 124, 628 (1948). 5. D.I. Blokhinstev, Acoustics of an Inhomogeneous Moving Medium (Gostekhizdat, Moscow, 1946). 6. Lande, Geiger Scheel, Handbuch der Physik, Bd. XX, 453. 7. L.C. Kober, "Stérung und Stérbefreiung von Riickstrahlung in Wellenfeldern,” 217-225; "Riickstrahlung von Reflexions Kérpern in Wellenfeldern," 217, Osterr. Ing.-Arch. (1951). 8. C.K. Bachelor, Theory of Homogeneous Turbulence (Cambridge University Press, 1956) p. 123; the formula in the text is obtained by correcting for the scalar nature of the temperature fluctuations. 9. Lord Rayleigh, The Theory of Sound (Dover Publications, Inc., New York, 1945). 10. Wolfgang Grébner and Nikolaus Hofreiter, Integraltafel (Springer-Verlag, Vienna, 1949), 11. Bierens De Haan, Nouvelles Tables D'Integrales Definies (G.E. Stechert and Co., New York, 1939). 12. E. J. Skudrzyk, "The Scattering of Sound in an Inhomogeneous Medium,” Pennsylvania State Univ. (May 10, 1960). 13. V.I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill Book Co., Inc., New York, 1961). 14, A.M. Obukhov, "On the Scattering of Sound in a Turbulent Flow," Doklady Akad. Nauk SSSR, 30, 611 (1941). 15. V. A. Krasilnikov, "On the Propagation of Sound in a Turbulent Atmosphere," Doklady Akad. Nauk SSSR, Vol, 47, 486 (1945). 16. P.G. Bergmann, "Propagation of Radiation in a Medium with Random Inhomogeneities," Abstract, Phys. Rey., Vol. 69 (1946). 17. V. A. Krasilnikov, "On Amplitude Fluctuations of Sound Propagating in a Turbulent Atmosphere,” Dok- lady Akad. Nauk SSSR, Vol. 58, 1353 (1947). 232 Lecture 12 18, C.L. Pekeris, "Note on the Scattering of Radiation in Inhomogeneous Media,” Phys. Rev., Vol. 71 (1947). 19. A.M. Yaglom, "On the Local Structure of the Temperature Field in a Turbulent Flow,” Doklady Akad. Nauk SSSR, Vol. 69, 743 (1949). German translation in Sammelband zur Statistischen Theorie der Turbulenz, 141 (Akademie-Verlag, Berlin, 1948). 20. V. A. Krasilnikov, "On Fluctuations of the Angle of Arrival in the Phenomenon of Twinkling of Stars,” Doklady Akad. Nauk SSSR, Vol. 65, 291 (1949), 21. V. A. Krasilnikovy and K.M. Ivanov-Shyts, "Some Experiments on the Propagation of Sound in the At- mosphere,” Doklady Akad, Nauk SSSR, Vol. 67, 639 (1949). 22. A.M. Obukhov, “Structure of the Temperature Field in a Turbulent Flow," Izvest. Akad. Nauk SSSR, Ser. Geograf. Geofiz., Vol. 13, 58 (1949). German translation in Sammelband zur Statistischen Theorie der Turbulenz, 127 (Akademie-Verlag, Berlin, 1958). 23. H.G. Booker and W.E. Gordon, "A Theory of Radio Scattering in the Troposphere," Proc. I.R.E., Vol. 38, 401-412 (1950); see also, Scatter Propagation Issue, Vol. 43 (1955). 24, M. J. Sheehy, "Transmission of 24-kc Underwater Sound from a Deep Source,” J. Acoust. Soc. Am., Vol. 22, 22-24 (1950). 25. M.L. Levin, "Sound Scattering in a Slightly Inhomogeneous Medium," Zhur. Tekh. Fiz., Vol. 21, 937- 939 (1951). 26. L. Liebermann, "The Effect of Temperature Inhomogeneities in the Ocean on the Propagation of Sound,” J. Acoust. Soc. Am., Vol. 23, 563-570 (1951). 27. S.1. Krechmer, "Investigations of Microfluctuations of the Temperature Field in the Atmosphere,” Dok- lady Akad. Nauk SSSR, Vol. 84, 55 (1952), 28. H. Staras, "Scattering of Electromagnetic Energy in a Randomly Inhomogeneous Atmosphere," J. Appl. Phys., Vol. 23, 10 (1952). 29. V. A. Krasilnikov, "On Phase Fluctuations of Ultrasonic Waves Propagating in the Layer of the Atmos- phere Near the Earth,” Doklady Akad. Nauk SSSR, Vol. 88, 657 (1953). 30. D. Mintzer, "Wave Propagation in a Randomly Inhomogeneous Medium,” Part I, J. Acoust. Soc. Am., Vol. 25, 922-927; Part II, Vol. 25, 1107-1111 (1953). 31. A.M. Obukhov, "On the Influence of Weak Atmospheric Inhomogeneities on the Propagation of Sound and Light,” Izvest. Akad. Nauk SSSR, Ser. Geofiz., No. 2, 155 (1953). German translation in Sammelband zur Statistischen Theorie der Turbulenz, 157 (Akademie-Verlag, Berlin, 1958). 32. V.I. Tatarski, "On the Theory of Propagation of Sound Waves in a Turbulent Flow," Zhur. Eksp. i Teoret. Fiz., Vol. 25, 74 (1953). 33. V.I. Tatarski, "Phase Fluctuations of Sound in a Turbulent Medium,” Bull. Acad. Sci. USSR, Geophysics Series, No, 3, 252-258 (1953). 34. D. Mintzer, "Wave Propagation in a Randomly Inhomogeneous Medium,” Part III, J. Acoust. Soc. Am., Vol. 26, 186-190 (1954). 35, J. Van Isacker, "The Analysis of Stellar Scintillation Phenomena,” Quart. J. Roy. Meteorol. Soc., Vol. 80, 251 (1954), 36, F. Villars and V.F. Weisskopf, "The Scattering of Electromagnetic Waves by Turbulent Atmospheric Fluctuations,” Phys. Rev., Vol. 94, 232 (1954). 37. L. A. Chernov, "Correlation of Amplitude and Phase Fluctuations for Wave Propagation in a Medium with Random Irregularities,” Soviet Physics—Acoustics, Vol. 1, 94-101 (1955). 38. J.H. Chrisholm, P. A. Portman, J.T. de Bettencourt, and J. F. Roche, "Investigations of Angular Scat- tering and Multipath Properties of Tropospheric Propagation of Short Radio Waves Beyond the Horizon," Proc. I.R.E., Vol. 43, 1317 (1955). 39, D.S, Potter and S.R. Murphy, "Acoustic Fluctuation," Part I, Univ. of Washington, Applied Physics Laboratory, Report APL/UW/TE/55-12 (April 7, 1955). 40. G. Keller, "Relation Between the Structure of Stellar Shadow Band Patterns and Stellar Scintillation,” J. Opt. Soc. Am., Vol, 45, 845 (1955). 41. F.H. Sager, "Fluctuations in Intensity of Short Pulses of 14.5-kc Sound Received from a Source in the Sea,” J. Acoust. Soc. Am., Vol. 27, 1092 (1955). 42. R.W. Stewart, H.L. Grant, W.N. English, and C.D. Maunsell, "The Fluctuation of Sound Transmitted in the Ocean,” Pacific Naval Laboratory, Esquimalt, British Columbia, Interim Report No. PIR-7 (August, 1955), 43. L.A. Chernov, "Correlation Properties of a Wave in a Medium with Random Inhomogeneities,” Soviet Physics—Acoustics, Vol. 2, 221-227 (1956). 44, V. A. Krasilnikov and A.M. Obukhov, "Propagation of Waves in a Medium with Random Inhomogeneities of the Index of Refraction," Soviet Physics—Acoustics, Vol. 2, 103-110 (1956). 45, R.A. Silverman, "Turbulent Mixing Theory Applied to Radio Scattering," J. Appl. Phys., Vol. 27, 699 (1956). 46, V.1. Tatarski, "Microstructure of the Temperature Field in the Layer of the Atmosphere Near the Earth,” Izvest. Akad. Nauk SSSR, Ser. Geofiz., No. 6, 689 (1956). 47. V.1. Tatarski, "Pulsations of the Amplitude and Phase of a Wave which is Propagated in Weakly In- homogeneous Atmosphere,” Doklady Akad. Nauk SSSR, Vol. 107, 245-248 (1956). 48. G.R. Garrison, S$.R. Murphy, and D.S, Potter, "Underwater Acoustic Transmission Variations Caused by Thermal Layers,” Abstract, J. Acoust. Soc. Am., Vol. 29, 186 (1957). 49, V.N. Karavainikov, "Fluctuations of Amplitude and Phase ina Spherical Wave," Soviet Physics—Acous- tics, Vol. 3, 175-186 (1957). 50. E.R. Pinkston, M. J. Pollack, and J.R. Smithson, "Sound Fluctuations and Related Oceanographic Pa- rameters in an Estuary," Chesapeake Bay Institute, Johns Hopkins Univ. Report No. 57-6 (September, 1957). E. J. Skudrzyk 233 51. D.S. Potter and S.R. Murphy, "On Wave Propagation in a Random Inhomogeneous Medium,” J, Acoust. Soc. Am., Vol. 29, 197 (1957). 52. E. J. Skudrzyk, "Scattering in an Inhomogeneous Medium," J. Acoust. Soc. Am., Vol. 29, 50-60 (1957). 53. V.I. Tatarski, "Microinhomogeneities of the Temperature Field and Fluctuation Phenomena of Waves Propagating in the Atmosphere," Dissertation, Akust. Inst. Akad, Nauk SSSR, Moscow (1957). 54, R. Bolgiano, "The Role of Turbulent Mixing in Scatter Propagation,” IRVE Trans. Anten, Prop., AP-6, 161 (1958). 55. B. A. Suchkov, "Amplitude Fluctuations of Sound ina Turbulent Medium,” Akust. Zhur., Vol. 4, 85 (1958). 56. F. Villars and V.F. Weisskopf, "On the Scattering of Radio Waves by Turbulent Fluctuations of the Atmosphere,” Proc. I.R.E., Vol. 43, 1232 (1958). 57. M.A. Kallistratova, "Experimental Investigation of the Scattering of Sound in the Turbulent Atmos- phere,” Doklady Akad. Nauk SSSR, Vol. 125, 69 (1959). 58. L. A. Chernov, Wave Propagation in a Random Medium (McGraw-Hill Book Co., Inc., New York, 1960). ect hth anaemic y Dee tH Me eng Ca gah) erin ete ) r Wine Arey ty one i Cw ELA Re ee ta ey diy ST Vp wy } Lyte | mms Ket ’ 1 SHV LD ahenn Reneh o beards ya Tae en oa woite th cai tia bens jad yoo) Ino ae ll i v : d RS, ALARA irhait V IA 4g? D0 tie. t , \ j yy ‘ i] j } ' t > ¢ Le “ ye ae { i / : ; ‘ 6 i i i i ot « 1 ‘ a LECTURE 13 AMBIENT NOISE IN THE SEA AND ITS MEASUREMENT P.M. Kendig Ordnance Research Laboratory The Pennsylvania State University University Park, Pennsylvania U.S.A. 13.1 AMBIENT NOISE 13.1.1 Introduction It has been found that acoustic waves afford the best means for detecting underwater objects in the ocean. However, in any detection system there is an interfering source of noise or signal that sets a lower limit to the level of the signal it is desired to detect. There are several different types of interference. Very often this limitation is the self-noise of the detection system, which may be caused by the hydro- phone, the electronic system, or the vehicle with which the observations are made. In an active sonar detection system, the underwater object is detected by means of an echo due to transmitted acoustic energy reflected from the ob- ject. However, some of the transmitted acoustic energy is returned to the listening hydrophone, even if the sound waves do not encounter a target, be- cause sound is scattered back to the hydrophone from the surface, the bottom, and even from scatterers in the medium itself. This may be, and often is, the principal source of intez ference. There is still a third general type of interference, the only one to be dis- cussed here, known as the ambient noise. This is the interfering noise that is due to natural conditions or sources inthe ocean. It will be considered a property of the medium itself at the time and place of observation, irrespective of the hydrophone and the platform used to observe it. It is the composite noise from all sources present in a given environment; desired signals and noise inherent in the measuring equipment and platform are excluded. The ambient noise level is expressed in terms of the level of an "equivalent" isotropic noise field at the observing hydrophone. Such an equivalent field is one that would produce, at the output of the measuring system, a response equal to that produced by the noise actually present. Following is a list of the commonly recognized sources of ambient noise: 1. Thermal noise due to molecular agitation of the medium is especially 235 236 Lecture 13 important at high frequencies in deep water, since it limits the hydro- phone threshold above about 50 kc Sea-surface noise associated with waves is the dominant source of am- bient noise in open-sea deep water in a frequency range from about 100 cps to 50 kc and varies in level with sea state 3. Biological noise caused by snapping shrimp and other soniferous sea creatures occurs locally in shallow water when these organisms are present 4, Man-made noise, including that from distant ships and from industrial sources in and near busy harbors, is often the dominant source below 1 ke 5. Rain noise in and near storms 6. Shore noise produced by surf on coasts or reefs 7. Flow noise caused by current flow over rocky bottoms and hydrostatic pressure changes produced by waves 8. Terrestrial noise caused by earthquakes, volcanoes, microseisms, and distant storms to Noises from sources (7) and (8) are normally of very low frequencies. 13.1.2. Deep Water—Thermal and Surface Noise Since there exists such a variety of sources of ambient noise, one would expect a considerable variability in level as a function of frequency and con- ditions related to the production of the ambient noise and indeed this is the case. It is found that in any given region of the spectrum, one or more sources are dominant and the output of the remainder is so low by comparison as to be en- tirely insignificant. Thus, for example, the thermal agitation due to molecular motion in the water provides a lower limit for the ambient noise at all fre- quencies, but it is dominant only in the upper frequency region, above about 50 to 200 kc, depending upon the sea state. The thermal noise level that sets this limit has been shown by R.H. Mellen [1] to be L=-115 +30 logf in db relative to 1 d/cm? in a 1-cps band at a temperature of about 15°C, and at a frequency f in kc. In the complete absence of all other sources of noise, this is the equivalent noise pressure that would be detected by an omnidirectional hydrophone with an efficiency of 100%. At lower frequencies, roughly 1to 50 kcandhigher, depending upon sea state the most important source of noise in the ocean is sea-surface noise, which ap- pears to depend upon the speed of the wind and on sea state. The first extensive measurements of ambient noise over this frequency region appear to have been made during World War II. The results of the measurements made during these studies were summarized in a series of curves known as the Knudsen curves [2]. In these curves, shown in Fig. 13.1, the spectrum of deep-water noise is plotted as a function of sea state and frequency. An extrapolation of the experi- mental data extends them to the thermal noise limit, which is also indicated. The principal characteristic of deep-water ambient noise is its variation with sea state and wind speed. At all sea states it is noted that the spectrum level decreases about 5 db/octave. It is also found that the intensity of ambient P. M. Kendig 237 ~—~THERMAL-NOISE LIMIT FOR AN OMNIDIRECTIONAL HYDROPHONE OF UNIT EFFICIENCY PRESSURE LEVEL IN I-CPS BAND (db vs | dyne/em®) “I29 10 100 FREQUENCY (kc) Fig. 13.1. Deep-water ambient noise levels (Knudsen curves). noise over this frequency range varies approximately as the 1.8 power of the wind speed. This variation indicates that the noise originates at the surface, but very little is known about the mechanism by which it is generated. The breaking of waves may be the primary contributor to this noise; but, for sea states below those at which waves break, some other mechanism for the pro- duction of noise must be postulated. In the absence of peculiar occurrences such as biological noise cr the noise due to falling rain, this type of noise is dominant. At lower frequencies, somewhere below 1 kc, the variation with frequency is decreased and the levels are no longer greatly dependent upon wind force. However, at still lower frequencies, the ambient levels appear to increase more rapidly as the frequency is lowered. The variation of ambient levels with depth in deep water was obtained by Lomask and Frassetto [3] with the Bathyscaphe Trieste. These measurements, which covered only the low frequency range up to about 300 cps, indicated a rather strong depth dependence except in calm seas. The level was shown to decrease by almost 16 db from the surface to a depth of 3000 m for a sea state of 2 and a relatively narrow band centered at 68 cps. The levels decreased with depth at other frequencies in this range but to a lesser extent, the decrease being only about 6 db at 10 cps. The measurements also indicated some strati- fication effects, but it did not seem that these were associated with the sound channel. Wenz [4] has recently shown a very interesting variation of low-frequency acoustic ambient noise levels in the ocean. His studies reveal a periodic varia- tion in underwater acoustic ambient noise levels at frequencies between 20 and 100 cps which has the following characteristics: 238 Lecture 13 1. Frequency. The fundamental frequency is seven cycles per week, i.e., one cycle per day. The fundamental period agrees closely with the solar day. 2. Amplitude. Amplitudes are relatively small in most cases, the over- all change in level being 1.5 to 5 db, and the phenomenon is often masked by other sounds such as ship traffic noise. However, changes of 10 to 20 db at one location during the summer solstitial period were observed. This is an extreme Case. 3. Phase. Maxima occurred at approximately midnight, local-zone stand- ard time, and did not shift from day to day as do the tidal maxima. 4, Waveform. The harmonic content varies with location. A second har- monic (14 cycles per week) was relatively strong and so phased as to give a second maximum at approximately noon, local time. In some cases, aS many as seven harmonics were found. The periodic variation has been observed each season of the year. No marked seasonal dependence was evident except at one location. Here the variation was a maximum at approximately the time of the summer solstice. The periodic variation has been observed at six locations, including sites in both deep and shallow water, both near to and remote from shore, and extend- ing over three time zones (45° longitude). Wenz has no explanation for this variation, although he has apparently ex- plored every possibility that comes to mind. He has considered wind-speed time patterns, tidal changes, variation in system sensitivity of performance, ship traffic noise, biological noise, and seismic activity. None of these seem to pro- vide any logical clues. The close agreement of the period of these variations with the period of the earth's rotation suggests the possibility of an extra- terrestrial connection. For example, the intensity of cosmic radiation has a diurnal variation with a maximum near noon. But what mechanisms can account for an increase in noise level whenthere is a decrease in the intensity of cosmic radiation ? 13.1.3. Shallow Water—Man-Made and Biological Noise In contrast with the deep-water ambient noise levels, which are compara- tively well defined, the ambient noise levels in coastal waters vary widely: For this reason, only very rough predictions of expected ambient levels can be made, However, the deep-water levels do define a lower limit for the shallow-water levels. Except for those that also occur in deep water, the two most important sources of noise in coastal waters are soniferous marine life and man-made disturbances, such as those caused by ships and industrial installations on the adjoining shores. The noise produced by marine organisms has been studied extensively since the beginning of World War II. More recently, the occurrence and acoustic char- acteristics of soniferous life in the Atlantic and Pacific oceans have been studied and the results summarized by M.D. Fish [5, 6]. Many types of marine or- ganisms are known to produce sound, but it has not been possible to associate P.M. Kendig 239 PRESSURE LEVEL IN I-CPS BAND (db vs | dyne/cm*) PRESSURE LEVEL IN I-CPS BAND (db vs | dyne/cm?) CROAKERS (late May and early June) IF CROAKERS (early July) AVERAGE SNAPPING SHRIMP NOISE KNUDSEN CURVES, ~~Z_ SEA STATE 6 / | @ (e) 1 Xo) (e) -50F a = -60F De oe -70- ar —~___,SEA STATE 0 ee ee ee eee) Ol | 10 100 FREQUENCY (kc) Fig. 13.2, Ambient noise levels produced by croakers and snapping shrimp. HIGH-NOISE AREA (entrance to New York harbor in daytime) AVERAGE-NOISE AREA (upper Long Island Sound near ship lane) DEEP-WATER NOISE FOR -50- A NO. 2 SEA STATE -60- ge -7ob -gol Cansei ee 1 it 1 Ht To eel 1 1 TREE TICS FREQUENCY (kc) Fig. 13.3. Ambient noise levels in the presence of ship sounds. all observed sounds with the particular marine animals that make them. Two types of marine animals, snapping shrimp and croakers, are known to produce a chorus of sound that can maskdesired signals. Shrimp are common in shallow, 240 Lecture 13 hard-bottomed tropical waters, whereas croakers occur predominantly in Chesa- peake Bay and other East Coast bays of the United States. Figure 13.2 shows typical ambient noise levels produced by croakers and snapping shrimp. It can be seen that biologically produced noise does extend into the frequency range of interest to sonar. Man-made noise may be predominant in busy harbors, shipping lanes, and many coastal locations, particularly at lower frequencies. During the war, many measurements were made of ambient levels in bays and harbors in the United States and Great Britain and near some Pacific Islands. The results of these measurements are summarized in NDRC Division 6 Report No. 3 of the Survey of Underwater Sound. The outstanding characteristic of this coastal ambient noise is its great variability from place to place in the same harbor and from time to time at the same place. Figure 13.3 shows typical ambient noise spectra for both a noisy and an average location in comparison with the deep-water am- bient noise level for a No. 2 sea state. 13.1.4. Rain Noise Falling rain, hail, and snow may be expected to increase ambient noise levels. Teer [7] observed an increase of from -62 to -50 db relative to 1 d/cm? in a 1-cps band in a No, 2 sea state at 19.5 kc due to steady rain. Heindsmann, Smith, and Arneson [8] observed the noise changes caused by the passage of two heavy rainstorms over a hydrophone system located 4 ft above the bottom in 120 ft of water near the eastern end of Long Island. During these observations, a recording was made and analyzed for the fall of 0.52 in. of rain in 90 min; the results are shown in Fig. 13.4. AMBIENT NOISE DURING RAIN AMBIENT NOISE BEFORE AND AFTER RAIN PRESSURE LEVEL IN I-CPS BAND (db vs | dyne/cm*) -70F Fale it =] JL LILI it 1 AR ILILILIVILt 1 | es ee | Ol | 10 100 FREQUENCY (kc) Fig. 13.4. Ambient noise levels produced by a rainstorm that precipitated 0,52 in. in 90 min. P.M. Kendig 241 The available information indicates that, at a frequency of 10 kc, rain can raise the average underwater noise level 15 to 25 db above the level indicated by the Knudsen curves for a given sea state. 13.1.5. Directional Characteristics It has been commonly assumed that ambient noise is isotropic; that is, the orientation of a directional hydrophone would have no effect on the detected level. However, R. J. Urick [9] has shown that for sounds originating at the surface, the variation of sound level with tilt angle will depend upon the directional char- acteristics of the hydrophone and the laws governing the radiation from the sea surface. He assumed the radiation to be distributed according to some power n of the cosine of the angle of radiation measured from the vertical. This analy - sis showed that for n equal to 0,1, and 2, the ambient levels measured by a searchlight hydrophone will vary with tilt angle. The directional characteristics of ambient noise at ultrasonic frequencies in water depths of 600 ft and hydrophone depths of 100 ft have been studied at the Ordnance Research Laboratory of The Pennsylvania State University. Meas - urements made with a searchlight hydrophone indicate that the ambient noise level measured in a vertical plane has two different characteristic distributions that appear to be functions of sea state. The data at sea states 1 and higher show the ambient noise level to be highest in the quadrant between the horizontal axis and the vertical axis, normal to the surface. The data taken at sea-state zero show that the peak in the ambient noise level usually occurs in the horizontal plane. A few exceptions to this do show a distribution at zero sea state similar to that obtained at the higher sea states. It would appear then that a transition between these two characteristic distributions occurs within the range of zero sea state. It was found that the distribution in the vertical plane was not strongly dependent on hydrophone depth at 60 or 100 ft. The maximum levels were sometimes as much as 10 db higher than the levels obtained with the hydrophone axis directed horizontally. These measure - ments also indicate that the levels are in close agreement when the hydrophone is directed either horizontally or vertically upward. This behavior did not fit any cosine law very well, but in some cases it tended to agree with the cos"9@ law where n has a value somewhere near unity. The directional distribution of ambient noise in the ocean has been studied recently and more extensively by the Marine Physical Laboratory of the Scripps Institute of Oceanography. This study is reported by B.A. Becken [10]. A 32- element, three-dimensional receiving array of hydrophones was employed, arranged in the form of a great stellated icosahedron and operating in the fre- quency range of 750 to 1500 cps. The 9-ft-diameter array was suspended from floats in from 1000- to 2000-fathom deep ocean and at array depths between 150 to 1000 ft. The digital multibeam steering (DIMUS) technique used in conjunction with this array provided 32 simultaneous searchlight patterns with principal axes distributed uniformly over all possible directions (47sr). All 32 hydro- phones were used in forming each beam. More detailed discussions of this sys- tem are given by V.C. Anderson [11, 12]. 242 Lecture 13 The results of these measurements indicated both an azimuthal and a vertical variation in the ambient noise. Azimuthal variation was observed principally in the outputs of array beams directed in the upper hemisphere. The distri- butions normally were elliptical in shape. It was observed that the maximum beam output for a given elevation angle usually aligned itself with the wavefronts of the swells while minimum outputs were perpendicular to the swells. This fact suggests a nonuniform radiation pattern of the whitecap or wavelet source; transmission in directions normal to the wavefront is impeded by the troughs, while lateral transmission along the ridges is less affected. The variation of the ambient in the vertical plane was generally found to be much greater than that in azimuth. Except for very low sea states, for which the array output was nearly constant for all directions, the array output was generally much larger when the beam was directed vertically upward. Figure 13.5 is one example of the true-field vertical ambient distribution at a depth of 560 ft in 2000 fathoms of water for a No. 3 sea state. In this figure, corrections have been made for the finite beamwidths of the arrays. From the nature of the distribution shown in Fig. 13.5 and other similar re- sults, the following picture of the mechanism ofnoise generation and distribution in the ocean has been constructed. Noise in the deep ocean is presumed to be a superposition of two fields. The first is that which exists at sea-state zero prior to the development of the wave motion and/or whitecaps. Its distribution 0° 30° 60° 120° Fig. 13.5. True-field vertical distribution (No. 3 sea state; three-array depth, 560ft). P.M. Kendig 243 is isotropic and its origin is not yet established. The second source of noise is generated by wave motion and whitecaps at the ocean surface. The equivalent surface radiator is highly directional in the vertical plane when azimuthal ef- fects are averaged. The directionality can possibly be attributed to the ocean waves and swells functioning in a manner analogous to angular focusing re- flectors. In addition, the ocean swells impede transmission at shallow trans- mission angles in directions normal to the wavefronts of the swells. It is further postulated that the noise intensity at a given point in the ocean caused by the equivalent surface radiator arrives by both a direct-ray path and single-bounce path experiencing specular reflection at the ocean bottom. By taking into account the bottom-reflected energy and the attenuation due to spherical spreading and absorption occurring over the separation between radiator and receiver, it is possible to evaluate S(6) which is the radiated -noise intensity due to unit incremental radiating surface at one yard. The quantity S(@) is markedly directional in the downward direction and can be represented approximately by the expression: 4 ((cos 9Y2° — 9/1 F420 < A < 70° © =) cos?6 for70° < 6 < 90° Figure 13.6 is a plot of a reasonable approximation of S(@) superimposed on the experimental data. OCEAN SURFACE SS Fig. 13.6. Surface source level re normal to ocean surface, 244 Lecture 13 13.2. THE MEASUREMENT CF AMBIENT NOISE We have seen that at high frequencies the ambient noise is dominated by thermal noise and represents the lowest detectable signal possible with an omnidirectional hydrophone of 100% efficiency. However, at lower frequencies (below about 40 kc), the sea ambient due to other causes and that due to thermal noise diverge about 11 or 12 db/octave as the frequency is reduced. Thus, it should become increasingly easy to measure the sea ambient as the frequency is reduced below 40 kc. However, there are other factors which tend to counter this advantage. The principal one is the reduction in the acoustic loading on the hydrophone for those cases where the wavelength is much greater than the di- mensions of the hydrophone. Since this loading varies as the square of the fre- quency in the low frequency range, itis quite incapable of measuring the thermal noise. But with proper attention paid to allthe design parameters, the equivalent noise pressure may be kept well below the sea-surface ambient in the low frequency region. The equivalent noise pressure of a hydrophone is that acoustic pressure due to plane sound waves which would produce the same open-circuit voltage across the terminals of the hydrophone as is produced by the thermal noise of the hydrophone in a 1-cps band. A hydrophone for broad-band underwater sound measurements should be essentially omnidirectional and have a flat, free-field voltage response over the frequency range. Section 13.3 indicates those factors which determine the equivalent noise pressure ofa linear hydrophone that obeys the reciprocity re- lation, that is small compared with the operating wavelength, and that operates in a frequency range well below that which would permit any self-resonances. These are the characteristics required for omnidirectionality and flat response, and are quite easily attained with several shapes of piezoelectric transducer elements—especially those made of electrostrictive ceramic materials. Three shapes will be considered: a hollow spherical shell, a hollow circular cylinder loaded on the cylindrical surface, and a flat circular disk loaded on both cir- cular surfaces. A number of approximations were made to better exhibit the Significance of each of the parameters. Details of the development are given only for the spherical shell, but the results are given for all three in Table 13.1. The results shown in Table 13.I do not include mechanical losses; but in a well-designed transducer these losses should have negligible effect at these low frequencies, which are well below all hydrophone resonances. The expressions for the efficiency show that it is strongly dependent upon the frequency and physical size of the transducer. For any present piezoelectric ceramic transducer, the second term in the denominator is small compared with the first. Thus, the efficiency is, approximately, in direct proportion to the square of the electromechanical coupling coefficient and inversely propor- tional to the loss tangent. Note that 1~—k2 does not differ greatly from unity, since k2 is always less than unity and is usually fairly small. However—and this is significant—if the coupling coefficient approaches unity, or if the loss tangent approaches zero, the efficiency approaches 100%. This demonstrates the important role played by each of these parameters. P. M. Kendig 245 Table 13.1. Electroacoustical Relationships for Three Types of Piezoelectric Transducers Electroacoustical efficiency Square of equivalent noise pressure pora(1 —a)k? kT ([2bE tan 5(1 — k2)? + pw%a‘(1 — o) k2/v) Square of free -field voltage response Transducer shape a2(1 — 0) k? Sphere TOOT": # 2vbE tan 6(1 — k?)? + pworar(1 -o)k? moa'(1 — o)k? 2E¢ceo 3_37,2 2y2 3)3)7,.2 2,2 Cylinder po athe — kT ([2bE tan8(1 — k2)? + pw%a*1k?/v) ak. 2vbE tan 8(1 — k2)* + pw°alk2 Toa [ke Eeo 32,2 e252) 3.2), 72 2,2 Senda || ———— Hb nO Gs lay pw et ee) 457k? vE tand(1—k;)° + pw°a’ bk ma’ whke Ee Since the square of the equivalent noise pressure varies inversely with the efficiency, it depends upon the same physical properties and transducer dimen- sions as does the efficiency. For all three transducer types, if the second term in the numerator is neglected, which may be done without materially affecting the results, it is seen that the square of the equivalent noise pressure varies inversely as the frequency. This assumes that tan is a constant for all fre- quencies, which is not necessarily true. Again, note that if tané approaches zero or if k, approaches unity, P? approaches the value 2 P? & e7e which is just the thermal-noise limit of the ocean. The last group of expressions presents the free-field voltage response in terms of the same parameters. It should be noted that 4, does not depend upon either the frequency or the medium; it does depend upon the modulus of elas- ticity, the dielectric constant, and the electromechanical coupling coefficient. It also depends upon some dimension of the transducer: for the hollow sphere and cylinder, it depends only upon the radius; and for the flat disk, it depends only upon the thickness. When using these relationships, any single consistent system of units may be used for the efficiency and the equivalent noise pressure. Since M, is usually expressed with a mixed system of units—namely, volts per microbar—a con- version factor must be used. For example, if the cgs-esu system is used, the results must be multiplied by 300 to obtain the usual volts per microbar. It seems worthwhile to re-emphasize the point that the free-field voltage response is definitely not an indication of the ability of a hydrophone to measure low-level signals, but that either the efficiency or the equivalent noise pressure is an essential indication of this ability. This is not to say that the free-field voltage response is unimportant, because low-level signals must be amplified to be measured. Now, the free-field voltage response depends upon the hydro- phone impedance, and this impedance, relative to the input impedance of the amplifier, is important if one is to take full advantage of the threshold sensi- 246 Lecture 13 tivity. This is especially significant if one wishes to detect signals over a broad band of frequencies. If a low equivalent noise pressure is the principal consideration in the de- sign of a low-level, low-frequency listening hydrophone, then the cylindrical hydrophone should be as large as possible, and have a wall as thin as possible. However, the size will be limited by the requirements of omnidirectionality and absence of resonances. The wall must not be so thin as to be crushed by the hydrostatic pressure to which it will be subjected. A hydrophone, shown in Fig. 13.7, and intended for operation at frequencies up to 3 kc was designed in accordance with these principles. It consists of four barium titanate cylinders that are coaxially mounted with acoustic isolation spacers between the elements. All four cylinders are encased in a rubber boot which is closed at both ends with heavy metal plates. Each cylinder is 2 in. long, 6 in. in diameter, and has a 0.2-in. wall. The barium titanate cylinders are KY) CABLE SEAL GUIDE STUD TOP END PLATE PHENOLIC RING Vz ie ma ry“ SN Co kark ——) SSyI 2222 QS (x io a Y2 A. REQ x WN = oS IS a LLLILLL LLL LAL ALLL LL (Z TL &re LF LF LF LT LE. 4 i 4 4 7; NT RK SNS G a PHENOLIC CYLINDER (LZZLLLL IES NYA LLL ZINN , N WS LILLL/ os \ LG LD LP LED LD LP é LT LD ED LA LT AGED ED AP LTT PF LDA N e RUBBER BOOT THREE SUPPORT AND CYLINDER LOCATION POSTS BARIUM TITANATE CYLINDER CLAMP BOTTOM END PLATE Fig. 13.7. Sectional view of hydrophone. P. M. Kendig 247 connected in series in order to achieve a high value of the sensitivity and con- sequently a high impedance. (The hydrophone has successfully withstood hy- drostatic pressures of 300 psi.) The four cylinders could be connected in several different series—parallel combinations which would provide various other im- pedances. Since the free-field voltage response varies as the square root of the impedance, this device may be used for adjusting the response. However, all such combinations will still give the same equivalent noise pressure. In this case, the cylinders were all series connected so as to achieve a high response and a high signal-to-noise ratio for the hydrophone amplifier combination. One very versatile means of controlling the impedance is to polarize the cylinder circumferentially in sections by means of electrical conducting stripes inside and outside the cylinder parallel to the cylinder axis. Since both the polarization and the field are now in the same direction (circumferential), the transducer also has a higher coupling coefficient than when it is plated inside and outside in the more usual manner (as was the case for the transducer described here). Following is a summary of the most significant acoustic characteristics of the hydrophone shown in Fig. 13.7, all of which appear to meet the design re- quirements over the specified range of 100 to 3000 cps. 1. Free-Field Voltage Response. -78+1.5 db re 1 v per pbar over the frequency range of 100 to 8000 cps. 2. Directionality. Omnidirectional within +1 db in all planes for fre- quencies up to 3000 cps. 3. Equivalent Noise Pressure. Varies from —91 to -102db rel pbar for a 1-cps band from 100 to 3000 cps, which is about 52 to 38 db, respectively, below the ambient noise levels of zero sea state. 4. Hydrophone Impedance. The impedance is essentially that due to a Capacity of approximately 0.01 uf. This section presented guide lines for designing a hydrophone with a low equivalent noise pressure and means for varying the hydrophone impedance in order to match the amplifier. Now the question is, can one detect a target that has a level over a band of frequencies lower than the ambient noise over the same band ? Here we will not consider correlation techniques or other similar devices, but just straight listening. The answer to this question is definitely affirmative, provided the target is localized in space. Hydrophones with radiating areas whose dimen- sions are large compared with the wavelength of sound in the medium have directional properties. The best example is the circular piston which has the so-called searchlight pattern. The directivity factor is the ratio of the intensity on the main beam of such a transducer at a fixed distance r to the average in- tensity over a sphere with a radius equal to r. For a circular piston with a diameter greater than the wavelength the directivity factor is approximately = aa DAG: where d is the diameter of the circular piston and A is the wavelength of the sound. If one substitutes this value in Eq. (10) of Section 13.3, this rather re- markable expression is obtained: 248 Lecture 13 a Cae | ENON SID Cc wCotan d © R R=— a2 Fig. 13.8. Equivalent transducer circuit for low frequencies, The first factor on the left is the equivalent sound intensity of the ambient thermal noise for a 1-cps band and the second factor is the area of the radiating face. Therefore, this expression states that for a 100%-efficient transducer, the ambient thermal noise contained in a 1-cps band is equivalent to a rate of flow of acoustic energy equal to kT, which, as we know, is the energy of one de- gree of freedom and is less than the kinetic energy of a single gas molecule.* Note especially that this is true no matter how large the radiating face of the transducer. On the other hand, Eq. (9) of Section 13.3 shows that the sensitivity or free-field voltage response of a hydrophone varies as the square root of the directivity, and hence it does increase with the size of the radiating face. Thus, we see that, at least for ambient thermal noise and indeed for any isotropic noise, an increase in the directivity provides an equivalent increase in the signal to ambient-noise ratio when the main beam of the receiving hydrophone is on the target. 13.3. FACTORS THAT DETERMINE THE EQUIVALENT NOISE PRESSURE, FREE-FIELD VOLT- AGE RESPONSE AND EFFICIENCY OF A TRANSDUCER AT LOW FREQUENCIES [13] 13.3.1. The Equivalent Circuit and the Efficiency Consider a thin-walled hollow sphere of radius a and wall thickness »b that is vibrating in the radial mode at a frequency well below resonance. At these frequencies, the equivalent circuit may be represented by the circuit diagram shown in Fig. 13.8, where Co is the clamped capacitance, C is the motional ca- pacitance, R is the resistance resulting from the mechanical load R;, XK is the stiffness, a is the electromechanical transformation ratio, tan 6 is the loss tan- gent (ratio of clamped resistance to clamped reactance), and is the angular frequency. The purely mechanical losses will be omitted in this discussion. At the low frequencies under consideration, the impedance is almost en- tirely capacitive. Indeed, from impedance considerations alone, the resistance *This expression appears to have the units of energy, because the bandwidth which has dimensions of reciprocal time was taken to be unity. P. M. Kendig 249 R is perhaps the least significant; yet, as a sound projector, it is the most important because the energy delivered to this element represents the radiated acoustic energy. Therefore, the value of this element, relative to the other re- sistive elements, determines the efficiency and, hence, the equivalent noise pressure of the transducer. Examination of the equivalent circuit of Fig. 13.8 shows that the electrical input admittance is ; V 2G, tand + jaCs +e Ons jo€ (RoC)? toll and since RaC «<1 at these low frequencies, * Y =@Cp tand + R(@C)? + ja@(C + Co) Again, since w(C + Co) > [wCp tand + R(@C)*], 2 wCy tand + R(wC) (1) Rao Ban= Bo ice arC= Gyr Since the second term is that portion of the series resistance produced by acoustic radiation, the efficiency is simply this term divided by R7, or Rw?C? See Sa ESE RO 2 @Cy tand + Rw*C (2) 7 Now, R; depends upon the specific acoustic impedance of the medium (py) and the dimensions of the transducer. At low frequencies, where the radius is con- siderably smaller than the wavelength, the expression for the real part of the mechanical radiation impedance is approximately R, = Ampaso (3) Vv where p is the density and vis the sound velocity of the medium. For a thin-shelled hollow sphere, the stiffness is approximately 87bE’ (4) where E’ is Young's modulus of elasticity and o is Poisson's ratio. The modulus E'is the short-circuit or zero-field modulus, and it is related to the open-circuit or zero-electric-displacement modulus E by the relation E'= E(1 -k?) (5) where k, is the electromechanical coupling coefficient. This may be expressed approximately by 2) Co eG Gh (6) For a thin-walled hollow sphere, the clamped capacity is approximately 2 Cy = cents (7) *The equality sign (=) will be used throughout, even though most expressions are not exact equalities. 250 Lecture 13 where ¢« is the dielectric constant and «9 is a constant whose value depends on the choice of units. Expressions involving Eqs. (3) through (6) and the electro- mechanical transformation ratio a may be substituted in Eq. (2) to give the fol- lowing expression for the efficiency, porai(1 —o)k 2 Se een Nar eee 8 2vbE(1 — Ke tan d + po a(1 = o)k?2 ‘) 7 13.3.2. The Free-Field Voltage Response and Equivalent Noise Pressure It is now desired to obtain expressions for the free-field voltage response and the equivalent noise pressure in terms of the same parameters. As a con- sequence of the reciprocal properties of the transducer, the former is given by fp =) ee (9) ™pv where A is the wavelength of sound in the medium and Dis the directivity factor, which will be taken equal to unity for the assumed conditions. It is usually necessary to amplify the low-level output of a hydrophone, and no matter how well an amplifier is designed, there still remains a residual output produced by thermal noise in the conductors of the input circuit. In the ideal case, this residual output will be entirely due to the hydrophone. The open-circuit voltage in the hydrophone circuit developed by thermal agitation in a 1-cps band is given by Johnson [14]: Ey =V4kTRr where k is the Boltzmann constant and T is the absolute temperature. Now, the equivalent noise pressure is defined as the equivalent acoustic pressure produced by sound energy, in a 1-cps band, that will generate an open- circuit voltage in the hydrophone just equal to that produced by the thermal noise at the same frequency, also for a 1-cps band. Since the sensitivity in Eq. (9) is E,/P, where E, is the open-circuit voltage across the terminals of the hy- drophone resulting from an acoustic pressure P, it is possible to solve for E, and to equate this solution to the expression for the noise voltage above. Solving this equation for the pressure, we obtain the equivalent noise pressure Bee) eae (10) 2 A“nD The desired expression for the equivalent noise pressure is obtained by sub- stituting Eq. (8) in this expression. This result is pie kT[2bE(1 - k?)? tand + pwra‘(1 = a)k2/v] (11) : moa(1 — a)k? From Eq. (1) it is easily seen that the real part of the series impedance that is due to radiation is QR, — ee 12 (Ger (2) P. M. Kendig 251 and this is simply the product of the total series resistance and the efficiency. This would be true even if the purely mechanical losses were not neglected. Therefore, substituting this expression for R;7 in Eq. (9) and making use of Eqs. (8) through (7), the free-field voltage response becomes ae o)k2 Mo=\ 5 (18) The three quantities, 7, Mo, and P,, have also been obtained for two other shapes of piezoelectric transducers: a hollow, thin-walled cylinder loaded radially and a flat, circular disk radiating from both flat circular faces. For these cases, the radiation resistance per unit area was assumed to be the same as that of a sphere having the same radiating area. Further, the length / and the diameter 2a of the cylinder were assumed to be roughly the same order of magnitude. The results are given in Table 13.1. REFERENCES 1, R.H. Mellen, "The Thermal-Noise Limit in the Detection of Underwater Acoustic Signals,” J. Acoust. Soc. Am., Vol. 24, 478-480 (1952). 2. V.O. Knudsen et al., "Ambient Noise,” from Report No. 3, Survey of Underwater Sound (OSRD Report 4333, NDRC Report 6.1-1848), PB 31021 (September 26, 1944). 3. M. Lomask and R. Frassetto, "Acoustic Measurements in Deep Water Using the Bathyscaphe,” J. Acoust. Soc. Am., Vol. 32, 1028-1033 (1960). 4, G.M. Wenz, "Some Periodic Variations in Low-Frequency Acoustic Ambient Noise Levels in the Ocean,” J. Acoust. Soc. Am., Vol. 33, 64-74 (1961). 5. M. D.-Fish, "Marine Mammals of the Pacific with Particular Reference to the Production of Underwater Sounds,” Woods Hole Oceanographic Institution, Report 49-30 (1949). 6. M.D. Fish, "An Outline of Sounds Produced by Fishes in Atlantic Coastal Waters,” Narragansett Marine Laboratory, Special Report No. 1, 53-1 (January, 1953). 7. C.A. Teer, "The Influence of Hydrophone Directivity upon the Measured Value of the Ambient Noise Level in the Ocean," Underwater Detection Establishment, England, Report 65 (May, 1949). 8. T. E. Heindsmann, R.H. Smith, and A.D. Arneson, "Effect of Rain upon Underwater Noise Levels,” J. Acoust. Soc. Am., Vol. 27, 378-379 (1955). 9, R. J. Urick, "Some Directional Properties of Deep Sea Ambient Noise,” U.S. Naval Research Labora- tory Report 3796 (January, 1951). 10. B. A. Becken, "The Directional Distribution of Ambient Noise inthe Ocean,” Univ. of California, Marine Physical Laboratory of the Scripps Institution of Oceanography, S10 Reference 61-4 (March 7, 1961). 11. V.C. Anderson, “Arrays for the Investigation of Ambient Noise in the Ocean," J. Acoust. Soc. Am., Vol. 30, 470-477 (1958). 12. V.C. Anderson, "Digital Array Phasing,” J. Acoust. Soc. Am., Vol. 32, 867-870 (1960). 13. P.M. Kendig, "Factors that Determine the Equivalent Noise Pressure, Free-Field Voltage Response, and Efficiency of a Transducer at Low Frequencies," J. Acoust. Soc. Am., Vol. 33, 674-676 (1961). 14. J.B. Johnson and F.B. Llewellyn, "Limits to Amplification,” Bell System Techn. J., Vol. 14, 85-96 (1935), DISCUSSION DR. F.T. DIETZ, by way of augmenting the lecturer's remarks, mentioned the results of ambient noise studies being carried out at the University of Rhode Island in a shallow-water location. The main objective in the systematic measurements made was to find any possible seasonal variations and to deduce any possible correlations between the ambient noise spectrum and environmental parameters, such as wind speed and direction, tidal currents, etc. Some 864 spectrum determinations were made on a ‘'/-octave basis in the range 40 cps to 10 ke using a "bottomed" hydrophone in a water depth of ap- proximately 30 ft. The results revealed that after a critical value of the wind speed is exceeded, then the acoustic pressure levels are linearly related to the 252 Lecture 13 logarithm of the wind speed andthere isa frequency dependence with a maximum effect at approximately 600 cps. These results are similarto observations made by N.E.L. and groups in Canada and Britain. The data below 150 cps showed variations which could be associated with tidal current flow around the hydrophones. More recent measurements, in the same locality but at 25 cps using a 3-axis seismometer, can be related to the lunar tides, but also display a sensitivity tothe solar tides. In order to eliminate the noise arising from water flow, a systematic series of low-frequency meas - urements are planned with the seismometer buried in the bottom. DR. W.N. ENGLISH said that he would like to draw attention to the ambient noise measurements made by A. R. Milne of the Pacific Naval Laboratory under ice in the Canadian Arctic. The initial measurements * were made under smooth new ice and the continuous noise level was extremely low and well below the Knudsen sea-state zero shown in one of Dr. Kendig's slides. Below 30 cps, some noise effects were obtained, attributed to wind and seismic influence, but ob- servations generally were limited by instrument noise. A second operation was carried out in the spring of this year under old, rough, shore-fast ice in a water depth of 1300 ft, using greatly improved instrumentation. As before, the ambient noise level was found to be extremely low provided the ice was not undergoing cooling. On calm clear nights and on other occasions when the ice was contract - ing, very sharp transients were heard which echoed back and forth in spectacular fashion before disappearing. Depending on the rate of cooling, the transients were infrequent or gave rise to almost continuous noise. Dr. English thought that this form of impulsive noise was sufficiently different from anything found in the open ocean to provide some interesting problems. DR.D.E. WESTON doubted the existence of any connection between ambient sea noise and turbulent density variations and thought a more likely cause to be the variations of water height, i.e., surface waves, ignoring the effect of break- ing waves which could occur at higher sea states. Although the first-order pressure amplitudes due to surface waves will fall off exponentially with depth, yet, if standing waves exist, the second-order (or Miche) pressures will not show appreciable amplitude diminution. At the time of the maximum displace- ment in a standing wave, quantities of water have been raised from below to above the mean water level and expressed physically the Miche forces cor- respond to the vertical acceleration of these water masses, at a frequency double that of the surface wave. Longuet Higgins’ has given a theory of microseisms based on the Miche pressure variations. Dr. Weston then said that, for the explanation of ambient noise, it was necessary to consider the high-frequency or capillary waves and to demonstrate the occurrence of standing wave ripples. The latter may arise from the large beamwidth (approaching 180°) of waves generated by wind, especially in gusty conditions of variable wind direction. Reflection of ripples at the sharp crests of the gravity waves could also give a standing wave ripple "riding" on a gravity *J. Acoust. Soc. Am. (August, 1960). tPhil. Trans. Roy. Soc. London, Ser. A, Vol. 243, 857 (1950). P.M. Kendig 253 wave. This explanation is, of course, by no means a quantitative theory as yet, and such factors as the energy loss due to viscosity have to be considered, but Dr. Weston pointed out that it was encouraging to hear Professor Skudrzyk state (Lecture 12) that the Kolmogorov spectrum lawisquite general and is applicable to both ripples and ambient noise. DR.H. A. J. RYNJA commented upon the statement concerning the efficiency of hydrophones and said that their efficiency approaches 100% only at resonance, and below the resonant frequency will drop to a much lower value determined by the square of the coupling factor (k). The maximum value of k for the ma- terials now available is between 0.50 and 0.60 so that the efficiency of the hydrophone below resonance cannot be more than 30%. This means that for maximum sensitivity in the measurement of thermal noise a set of hydrophones with different resonance frequencies should be employed. DR. KENDIG: At low frequencies, which are well below any resonance and for which the wavelength of sound in the medium is large compared to the hy- drophone's dimensions, the efficiency will generally be low. In the case of typical ferroelectric materials, the low efficiency in this low-frequency region is due primarily to the dielectric losses. Thus, the loss tangent (dielectric losses) is just as important as the electromechanical coupling coefficient. On the other hand, if pure mechanical losses are large compared to the radiation losses, the efficiency will be low no matter what values exist for the loss tangent and the coupling coefficient, because the ratio of pure mechanical losses to radiation losses is independent of the loss tangent and the coupling coefficient. At low frequencies, it is usually possible to measure the ambient noise of the sea even if the hydrophone efficiency is quite low, because the sea ambient, even for zero sea state, is very much greater than the thermal noise. For example, at 1000 cps the zero sea-state ambient is about 60 db higher than that due to the thermal noise. Thus, it is quite possible to measure the sea ambient at all sea states with a nonresonant hydrophone up to at least several thousand cycles per second. “BRN MM te uns dE Mbt ots i a ‘Gh, thy Apa SR Ay ot iis See wkd a Mi-bliimeline! cum loongywremnuende ee eit ory nO huy eines Aeeang wail a Roh TURNED | Hae ered AoW a oe i y ’ 6 tienda ents i jane es rsvp ce ‘ ra i Pee coer a 1h, ya tops ivi taeg gable ad |} Jaw an@n’) ral ae Joe ah wih oe nee Uo al Hie =e il eee ort Sat ont . 'q09 Al To 9: lee j uy Oty Oia eae ‘ ‘uC 4 op mh ily AM Obert hy Lag Lia : ' © witht iat -] lage ers ' { or S25 wae 1 Ge Vi ead teller. el oe web iS Te nella a! by. bidiaiaal Jno yih } , U0 ert Phang ' fi a) : “i ‘ol SAC wot nr vit - Mi 4d aaa! Os Teil Met At \/ ard iW) eae + Mi ae, | “4 4 jodva rol wad = pv*? (1) where u’ and vy’ are the components of the fluctuating velocity in the direction of the main flow and transverse to it. The magnitude v*=,/ is defined as the root-mean-square average of the velocity components and is the shear velocity. This velocity v* determines the shear force near the wall or surface drag. The surface drag has been thoroughly studied for channels [2], plates [1], and even for rotating cylinders [3]. The experimental results show that the sur- face drag is approximately proportional to the square of the free-stream ve- locity uo. The surface drag can, therefore, be expressed as the product of the coefficient of drag cg and the square of the free-stream velocity: r= 7egpus (2) where p denotes the density of the fluid. The coefficient of drag proves to be practically constant; it is approximately equal to 3-107? whenever the flow is turbulent. It changes by only a factor of three when the velocity is changed by a factor of as much as 5,000. Since the surface drag is generated in the inner part of the boundary layer, we might expect that it would not directly depend on the curvature of the surface nor onthe size of the body that generated it. This conclusion is verified by measurements with rotating cylinders [3]. No dependence on the ratio of diameter to height was found. The fluctuating velocity v* can be estimated by equating the theoretical and the experimental results: 3 dca pus = 3.1073. pu = pv*? (3) or v* = 0.04 uo (4) E. J. Skudrzyk and G. P. Haddle 257 The shear velocity v* turns out to be very nearly equal to 4% of the free-stream velocity. This result is in good agreement with, for instance, Laufer channel measurements [2]. The shear velocity is 4% at the outside of the laminar sub- layer and then decreases linearly with the distance until it becomes Zero at the outer limit of the boundary layer. The shear velocity v* is connected with the nearfield noise pressure by an equation very similar to the well-known Bernoulli equation, the only difference being a modified constant: p=apv*? (5) Computations have been performed by Batchelor [4] fora region of homogeneous turbulence, and by Kraichnan [5] for a simplified model of a boundary layer. For the boundary layer, the factor '4 in the Bernoulli equation turns out to be the factor a of the order of magnitude 7. The constant a may be expected to de- pend slightly on the Reynolds number. The nearfield sound pressure that is generated by the velocity fluctuations is similar to the acoustic radiation pres - sure, or the stagnation pressure on a moving body, except that stagnation now is generated not by solid bodies but by the velocity gradients of the moving eddies. This pressure is proportional to the square of the velocity fluctuations and is, therefore, a second-order phenomenon in terms of the velocities. The spectral distribution of the nearfield pressure can be estimated in a very simple manner. The turbulent eddies are correlated over distances of the same order of magnitude as the boundary-layer thickness. Each one of the turbulent eddies that moves over the sensitive area of the hydrophone represents a pressure pulse whose magnitude is constant as long as the pulse is in full contact with the hydrophone and then decreases rapidly to zero when contact is lost. The spectrum of such a pulse is well known. It is practically constant up to a frequency » whose semiperiod is equal to the pulse duration t;. From then on, it decreases as sin(@t;/2) sin (f/f) aE (6) where t, = 5/uy = 1/f), uy being the flow velocity, 5 the space length of the pressure pulse, and f) the repetition frequency of the pulses. The low-frequency part of the spectrum is practically independent of the details of the pressure distribu- tion inside the pulse. It is proportional to the average value of the pressure during this interval. In contrast, the high-frequency part of the spectrum de- pends on the details of the turbulence. It is practically impossible therefore to predict the high-frequency spectrum with adequate accuracy. However, the experimental results show that the spectrum decreases inversely proportional to the second or third power of the frequency. Figure 12.10* shows the power spectra of the longitudinal velocity fluctua- tions u’ of the turbulence and of the Reynolds stress u'v'as given in [6] and [7] (for a point close to the wall, a flow velocity of 49 ft/sec, and a displacement thickness of the boundary layer of approximately 0.24 in.). The frequency f, is therefore 200 cps. As predicted, the spectral amplitudes are practically con- stant at low frequencies (particularly those of v’ andu'v’); they decrease ac- *See page 208 of this volume. 258 Lecture 14 cording to a -—*h power law (Kolmogorov) [8] for high frequencies and according to a -7 power law (Heisenberg law) [9] for very high frequencies. The curves show that, apart from relatively unimportant deviations at very low frequencies (or space wave numbers), the velocity fluctuations and the Reynolds stresses (that is, the velocity products uv’, etc.) have approximately the same spectral distribution. Similar results have been obtained for the power spectrum of the flow noise by M. Harrison [10], by W.W. Willmarth [11], and by the Ordnance Research Laboratory [12]. The spectral density of the turbulence noise may thus be considered to be constant up to a frequency uo/d determined by the ratio of the free-stream ve- locity to the thickness of the boundary layer. From there on, it may be expected to decrease inversely proportional to a certain power m of the scale of the turbulence or the space wave number; a different power law may then be ex- pected to apply in the viscous range. This power law may be deduced from the known laws of turbulence or deduced from the experimental results. The power spectrum of the pressure referred to unit frequency interval is thus known by Pte) = p3 (22) for @2W (7) 2 Sor os c soe (8) In Eq. (8), the frequency #0 at which the noise spectrum starts to decrease is expressed by the ratio of the free-stream velocity to a quantity 6 which is of the same order of magnitude as the boundary-layer thickness. The relation 6 =56*, where 6* is the displacement thickness of the boundary layer, seems to lead to very good agreement with the experimental results. This relation has therefore been assumed in all the following computations. The preceding considerations in conjunction with the pressure, Eq. (5), lead to the prediction of the spectral distribution of the noise pressure. The constant ps, however, remains unknown. This constant can be determined by computing the rms noise pressure (neglecting the viscous range): fea} wo Tas} a 2 2.2 da _ 2 dw 2(@o0\ dw p =ar -{ po) d= f cate |) p3(22) = (9) ty) 0 0 and by equating the result to the value given by the Kraichnan equation: 2 _ 0.75.10-° a2p2ug 5* |3(m—— (10) pPo=vV. . P uo 9} m ™m If this value is substituted above, the power spectrum P(w) of the noise becomes P(@) = 0.75-1075 a®p*uad*[3(m-2)] for @<@o (11) E. J. Skudrzyk and G. P. Haddle 259 and 2,2 6 1\ |] /27u.\n—-3 P(w) = 1.5-107§ = Fe) -2)(2e for w > @o Measurements with a small receiver lead to a value m=3 for the slope of the curves in the descending part of the spectrum. For m= 3 the expression in square brackets reduces to 1, and the power spectrum of the flow noise at low frequencies becomes proportional to the third power of the velocity and to the boundary-layer thickness; and proportional to about the sixth power of the ve- locity and inversely proportional to the square of the boundary-layer thickness at high frequencies. These predictions and the numerical values computed by the foregoing equation are in very goodagreement with the experimental results, as will be shown later. 14.3. THE RADIATED FLOW NOISE Lighthill's theory [13] leads to the computation of the farfield sound pres- sure. Unfortunately, the magnitude of this pressure can only be given in terms of higher order correlations, which have not yet been studied in detail. It has, therefore, not yet been possible to derive a correspondingly simple formula for radiation-field sound pressure generated by the turbulent velocity fluctuations. It will subsequently be shown that the sensitivity of a hydrophone to the flow noise nearfield decreases greatly with the diameter of the hydrophone. A large hydrophone is, therefore, practically insensitive to the flow noise nearfield. But a large hydrophone is sensitive to the radiation-field pressure that is generated by the unsteadiness and the decay of the turbulence. This sound field propagates inside and outside the boundary layer and is correlated over distances of about half a sound wavelength. Since the hydrophone is usually much smaller than the sound wavelength, it is fully sensitive to the radiated sound and records it as flow noise. A large hydrophone measures almost exclusively the true sound that is produced by the unsteadiness of the turbulence. 14.4. EFFECT OF SIZE AND SHAPE OF SOUND RECEIVER ON AMPLITUDE-VS-FREQUENCY CURVE OF FLOW NOISE Flow-noise pressure is a local, rapidly varying quantity and only a hydro- phone that is small in comparison to the scale of the local pressure fluctuation measures the true value of pressure generated by the turbulent velocity fluctua - tions. If this hydrophone is tuned to a narrow frequency band, its response becomes proportional to the Fourier component of the noise pressure in the received frequency band. It has beenshownby Taylor, Proudman [14], and others that the decay of the turbulence has only a minor effect on the nearfield noise pressure. It can be assumed that the turbulence is carried along by the flow, with a mean velocity UY not very different from the free-stream velocity of the flow. The frequency f of noise pressure received by the small hydrophone, and the space wave number x of the turbulence are therefore connected by the relation, Pal, aH 2b i ako (12) 260 Lecture 14 where A,, is the space wavelength of the pressure pattern that produces the noise band. Thus, the pressure fluctuations that give rise to a definite spectral com- ponent of the flow noise are no longer uncorrelated but correspond to a sinusoidal pressure pattern p = p(k) cos k(x-Ut) that moves in the direction of the flow. Thus, tuning the hydrophone destroys the randomness of the received signal. A hydrophone of finite size measures the average pressure over its area. If the hydrophone is infinitely narrow, but of a length 1,, this average pressure fluctuation is given by the integral 1,/2 F@)_1 p(k) cos x(é — Ut) dé = PL) sink aN sink Dh, ut ly ly ; Kit 2 2 1/2 — 2p(k) <3, Ka _ p(k) sin («1,/2) = ae sin 5 COS <$—arigy (13) where w=xU. The average value of spectral amplitude of the noise pressure over the hydrophone area is thus proportional to the infinite space spectrum p(x) of the pressure fluctuations in the boundary layer; p(x) alone determines the fre- quency component F(@) where w = Uk, whether the hydrophone is finite or infinitely small. The effect of the finite dimension of the hydrophone in the direction of the flow on the received pressure amplitude is represented by the factor sin(«l,/2) ~. [«l,\7? GA F é) (14) The maxima and minima in the pressure distribution cancel one another over the hydrophone area and the contribution of one pressure maximum, on the average, remains, irrespective of the length of the hydrophone; the contribution of this maximum is represented by the above formula. The longitudinal dimen- sions of the hydrophone become important as soon as the length of the hydro- phone is greater than one third the space wavelength 4,, of the turbulence that generates the noise. Doubling the length of a tuned hydrophone should then re- duce its relative flow-noise output by 6 db. This cancellation of successive maxima and minima introduces the factor 1/x? =(U/a)? in the frequency curve of the measured flow-noise power spectrum. If the hydrophone is of variable width, but of a width that is always less than the transverse correlation length of the pressure fluctuations, the integrand must be multiplied by the width. If the hydrophone is symmetrical with respect to its midpoint, the mean force on its membrane becomes U FO) - f eee =U) 1 ce = (a5) 0 The mathematics, then, is exactly the same as that for a shaded hydrophone array, the magnitude «/sin 6 being replaced by «/, and the shading function being E. J. Skudrzyk and G. P. Haddle 261 replaced by the width y(é) of the hydrophone. By properly shaping the hydrophone, the factor 1/l, of the preceding formulae can be changed into a factor (1/xl;)”, and the flow-noise sensitivity of the hydrophone can be made considerably smaller (as long as the nearfield pressure determines the received level). The flow-noise sensitivity of a hydrophone is thus a function of its shape, and the experiences acquired in shading hydrophone arrays can be used to reduce the received flow-noise level. For a circular hydrophone whose radius R is small in comparison to the transverse correlation length, the force on the hydrophone can be given by the following integral: 1 R = 2 rar p(k) cos xé ER? = poor? f cos (kRy) dy fia hi OE (16) R aT TET @«R where IT is the gamma function, and J: is the Bessel function of the first order. At higher frequencies, when xR > 1, the Bessel function can be replaced by its asymptotic expression, and 2 F = constant LOE = constant - Fo se (17) Doubling the radius now decreases the narrow-band noise level by 9 db. If the transverse correlation length of the eddies were independent of their longitudinal wavelength, the effect of the finite diameter of the hydrophone would reduce the flow-noise output by 9 db per frequency octave. A hydrophone whose width increases as the sine of the distance from its end, y = sin (18) 1 would yield an output ty a : (K)lilot Fo PS I (k) cos (kx) sin 2 dx = 2 k) -~—cos xk = EN, S 19 af p(k) cos (kx) T, x ace Tiare 1 ; elt 2 (19) The hydrophone shape shown in Fig. 14.1 is interesting from a practical point of view. Its flow-noise sensitivity is proportional to the integral a a+b 2a+b [rcosexae +f acosnxde + f (2a + b — x) cosKx dx 0 a a+b ~ Jy 2 sin? tina 28 +) a (20) K 2 2 K Fig. 14,1. Special hydrophone shape. 262 Lecture 14 The results of the preceding paragraph can also be deduced from the sta - tistical theory given by Corcos, Cuthbert, and Von Winkle [15]. The integral of Eq. (15) is identical with the solution of the equation given in [15], if the trans- verse correlation length is small in comparison to the width of the hydrophone. But the statistical solution cannot be evaluated in closed form when the width of the hydrophone becomes larger than the correlation length. However, it is easy to see that the hydrophone area can be subdivided into strips of width equal to the transverse correlation length of the pressure fluc- tuations. The contributions of all the strips willthen be uncorrelated and random in phase, and they will add energy. The sensitivity of a rectangular hydrophone that is broad in comparison to the transverse correlation length will, therefore, be given by sinkl, 5 [2 sink] [6 SF — = }7 eee Y ZI e kl, l, (0) 9 Kl, Ty cay Doubling the dimensions of the hydrophone then decreases its flow-noise output by 9 db, and doubling the frequency decreases the flow-noise output by 6 db. For minimum flow-noise sensitivity, the strips should beof optimum shape; but none of them should be rectangular, and it is immaterial whether they are symmetri- cal or not. The strips can be of the shape shown in Fig. 14.2, but the length J; of each strip has to decrease by more thana space wavelength A,, of the turbulence per each unit increase of correlation length 6,. For a frequency of 20 kc, a correlation length 5, equal to 0.1 in., and a velocity of 600 in./sec, al; 600 CL ee OURS EY Ly (22) dy 20,000-.0.1 3 Thus, the angle @ should be 45° at the greatest. The ends of the hydrophone should be somewhat tapered in the direction ofthe flow, as indicated. A properly DIRECTION OF FLOW Fig. 14.2. Optimum shading of a hydrophone. E. J. Skudrzyk and G. P. Haddle 263 shaped hydrophone can then be expected to have a flow-noise response propor - tional to Fi =? ae (@) Rll ( ) The power-spectrum decrease will be proportional to the fourth power of the fre- quency and to the square of the product of the linear dimensions of the hydrophone. A circular hydrophone, as a first approximation, may be resolved into a central strip and a number of shaded strips, n-1~n, the strips being all ofa width equal to the transverse correlation distance. The resulting force on the receiver, then, is given approximately by odes an gg aye LP. A a SL faire p=18,+4@-y24 nos +[75| \Z _ (00.4: ets (24) If the width of the receiver is much greater than the correlation length, the second term predominates as long as the frequency is not too high. The cir- cular hydrophone can therefore be expected to behave like a perfectly shaped hydrophone at the high, but not at the very high, frequencies. At very high fre- quencies, the flow-noise sensitivity of the circular hydrophone will probably increase again. A rectangular hydrophone is particularly sensitive to flow noise. The flow- noise sensitivity of a hydrophone can be considerably reduced (as long as the nearfield pressure determines the received level) by varying its width from a small value to a maximum in the middle and to a small value again at its end. In a hydrophone of this shape, the pressure maxima and minima of the noise pressure (Fourier components of the noise pressure) cancel one another to a higher degree as they are transported by the flow across the hydrophone area. The effect of varying the width of the hydrophone is similar to the shading of arrays of hydrophones. Its response outside the main maxima-—that is, for the higher frequencies of the turbulence—decreases considerably. Because of the approximate isotropy of the eddies, the flow-noise sensitivity of a perfectly shaped hydrophone can be expected to be reduced by a factor of _ | sin(kl;/2) 7 =| Ky11/2 | 2) Figure 14.3 shows a graphical representation of the square of this factor, which determines the received power spectrum, for a hydrophone that has a diameter 4.3 times the boundary-layer thickness. This curve is very nearly the same as the curve determined for the hydrophone sensitivity from Willmarth's [11] measurements. The range of these measurements, however, extends over only 1.5 decades (energy levels); therefore, this apparent agreement does not mean too much. However, the theoretical curve explains the steep slope over the range 0.5 <27f5*/Up < 0.8 that has been observed by Willmarth and Harrison and that has not been observed at frequencies greater than those of the buoyant-unit runs to be described later. Doubling the linear dimensions now reduces the flow-noise level by 12 db, and doubling the frequency reduces the spectral level by 12 db. 264 Lecture 14 Fig. 14.3. Effect of a circular hy- drophone on the received power spectrum of flow noise. [= ieee] nd 14 10-2 13 RELATIVE HYDROPHONE SENSITIVITY w87U —— The above theory is only partially borne out by the experiments as will be shown later. It has been assumed that the turbulence is homogeneous, so that it can be described by its space- and time-average microscopic properties. However, for the frequency analysis, filters are usedthat have a relatively great bandwidth and consequently a very short integrationtime. The frequency analysis therefore yields results that correspond to averages over very short time in- tegrations. For such short integrations the turbulence is far from being homo- geneous. Every individual bump of turbulence is recorded separately: the filters have forgotten all about the first bump of turbulence when they receive the second, and the cancelling-out effect described above seems to be limited, on the average, to the volume of one such bump of turbulence. This volume is ap- proximately the same as the volume over which the turbulent velocities are correlated. The analysis of turbulence may usually be designated as an analysis of the macrostructure of the turbulence; in contrast, an analysis of the flow noise seems to correspond to an analysis of the microstructure of the turbulence. 14.5. NOISE GENERATED BY THE SURFACE ROUGHNESSES As the velocity of the vehicle increases, the roughnesses become more ef- fective. Experimental results show the roughnesses shed eddies whenever they E. J. Skudrzyk and G. P. Haddle 265 penetrate the laminar boundary sublayer [16], that is, when the fluctuating ve- locity v* exceeds the value five. This Reynolds-number condition leads to the equivalent result that in a turbulent boundary layer, the surface OU ESI become effective whenever this height in inches becomes equal to 6- 10-* divided by the velocity of the vehicle Up in knots: h [inches] = 6 ee [knots] (26) If the boundary layer is not turbulent, v* has to be replaced by the true velocity Uph/d at the peaks of roughnesses, and the corresponding Reynolds-number con- dition becomes Uh 5h (27) or h? _ Sv _ 4.2. 1074 (28) Oo HS wp where UJ) is in knots and 6 is in inches. For a boundary layer of a thickness of 10-2 in. (as on the spherical head of a buoyant unit) and a speed of 42 knots, h/5= 0.1, or h= 1074 in., which is in good agreement with the experimental results. The eddies shed by the surface roughnesses may be expected to depend on the velocity gradient near the wall. They will be independent of whether the —_- — — 5 HYDROPHONE NO 3 8-014: ot SOtps 1/2 in DIA 3 ft from entrance of tes} section DBS re/ dyne/ cm?/ cps 1 ' ' 10 100 FREQUENCY IN KC Fig. 14.4. Flow-noise spectra as a function of speed. 266 Lecture 14 pu,> 8" 8" =0.105" AT 100 FPS, DIA OF HYDROPHONE LESS THAN 0.125" db M. HARRISON “ia = A WILLMARTH rey MA @ =50 FPS O = 100 FPS A =.200 FPS Pale DIA HYDROPHONE ate Sea = 1" DIA HYDROPHONE we SS Nan 10 100 Ol | #/(U,/ 8°) | Fig. 14.5. Flow-noise spectra in dimensionless variables showing the effect of hydrophone diameter. boundary layer is turbulent or laminar. However, the eddies decay rapidly in the laminar boundary layer, whereas in the turbulent boundary layer the eddies shed by the surface roughnesses increase the intensity of the turbulence in the boundary layer. 14.6. EXPERIMENTAL RESULTS Measurements of the boundary-layer noise have been performed in the test section of the Garfield Thomas Water Tunnel at the Ordnance Research Labora - tory and in Key West with the aid of two cigar-shaped buoyant units. Because of the great intensity of the flow noise, machinery noise is masked by flow noise and measurements can be performed in water tunnels, The curves shown in Fig. 14.4 were obtained in the test section of the Garfield Thomas Water Tunnel, which has a diameter of 122 cm. Hydrophones were mounted flush with the wall and the noise levels were analyzed in a frequency range from 60 cps to about 30 kc. Figure 14.4 shows the noise levels as functions of the frequency for various speeds. Figure 14,5 shows the same curves and additional ones for a larger hydrophone diameter represented in dimensionless variables, The curves obtained for a particular hydrophone size are almost coincident and the difference in the levels obtained for the two hydrophone sizes is about 12 db as predicted by the theory. Figure 14.6 reproduces the result of anarrow-band analysis of the noise. Machinery noise and wall vibrations would have generated spectral lines; how- ever, such lines do not appear in the spectrum. m ~ n > c Q = N SS > Q 3 Q i) vu = Q Q 2 i) No nN N | | { | i } l To we ee = : Sts es em SSS oe SAEs 2G eS a SS SS SS SS SS = sie fe Nf 20 CYCLES SE eo 7 2s lige reery, fee ees i ee oe ee ee a A a a * = - A is abe “4° 4 Sd =v == ; 4 aE ed es Sere oe et ee arc Oe ae ae ee Se J ae@rais 4 ° a = oe. or ere c UES ar eek eee iio: ==. == sa 2S SSS Se So SS ae meer oes lee SS Se 2 ee ee Ge Se Ge * 2 a sere 7-7 ar G es Oh oie 4 7 hPa its! Pe oD ee oan ai Le one Ba | it 6 1 f Ba 28 A | it si I : l jgsue MIL (ith HV 1% bh 2 li ny ol AI fo) / oO} { °) ad oO On So oa Oo N iy o a | Co ik 1 i oO | (a) \ oO GY cE i ratte \ i ie Hs wi Mn I HM WN HN oo... oe v2. é. Wi = SSS asa ——— Et 5 5 sq = aT ffl Pp all) LT | : 4 [iT Ha ELT I == 2S Se 2 ae — ae nt =" a =a SS ae a2) ae eee = Sass Sa == SS SSS Seas ateoen p 1 } q i ) y 1) S| 23 5° Se. 0- 1 12 13 14——15= 4 : f = FREQUENCY IN KILOCYCLES PER SECOND] =! E = =s Fig. 14.6. Narrow-band spectrum analysis of flow noise. So The noise generated in a frequency band around 24 kc by the surface rough- nesses has been studied with the aid of a rotating cylindex of a height of 42°), in. and a diameter of 17.2 in. Such a cylinder has a very thick boundary layer, and consequently generates little high-frequency boundary-layer noise. A rotating cylinder is, therefore, particularly suited to study the effect of roughnesses. * Figure 14.7 shows a number of curves that have been obtained for various types of roughnesses on the surface of the cylinder with a 2.5-in.-diameter hy - drophone. The noise level now exceeds that of the ambient noise at a much slower speed than in the previous case. Forthe same velocities, the flow noise produced by the rough surface is 20 to 50 db greater than that produced by the smooth, painted surface. Since nothing else has been changed, this greater noise must be attributed to the effect of the surface roughnesses. There is thus no doubt that roughnesses generate flow noise. For Grit No. 180, 80% of the particles have a height of about 5- 107° in. The critical speed [Eq. (26), where the roughnesses become effective] is therefore 2 knots or 1.08 m/sec. Ifwe extrapolate the curve for this kind of grit down to a speed of 2 knots (from whence the roughnesses *Rotating cylinder measurements have also been performed by L.N. Wilson [17]. Lecture 14 268 *\uoUNeeD adejIMS jo 10979 oy] Burmoys pseds Jo uotjouNj e Se aStou MOTY *Z*PT “SIA 93S/SY3S1SN Ob 02 YSGNITAD ONILVLOU {o}] 8 9 v cAn=d G3.LNIVd gvyAvD-d WL3W HLOOWS 1iy9 O09 ilyS os! gAn zd 160802090 O9i- O2I- ool- 08 - o9- Ov- 02- (Sd 9/2W2/ 3NAG |'34) SEO E. J. Skudrzyk and G. P. Haddle 269 would be expected to become acoustically effective), the noise level turns out to be -158 db relative tol d/cm?. This value may be considered as the equivalent of zero flow-noise level for the condition of the experiment. The other curves should then intersect with the zero flow-noise level, —158 db, at speeds equal to the corresponding critical values; and this indeed seems to be what happens if we allow for a small experimental error and for the fact that the energy of the background and that of the flow noise add up to the resultant noise level so as to change the shape of the curves at lower noise levels. Paint covers the smaller roughnesses, but in doing this seemsto increase the larger roughnesses with paint streaks. Yet the density of the larger roughnesses is relatively small and the roughness noises seem to be masked by the boundary-layer noise. This conclusion follows from the slope of the curve, which is only 18 db per speed octave. We may conclude that the roughness noise equals the boundary-layer noise at 24 kc at a speed that is about six times as great as the critical speed if the surface is densely covered with roughnesses, and at a correspondingly higher speed if the roughnesses are widely spaced from one another. Figures 14.8 and 14.9 show measurements obtained with buoyant units. The units were about 5 yards in length and 19 in. in diameter. Each was equipped with six hydrophones and a seven-channel tape recorder. Theory predicts that the spectral level of the low frequencies is proportional to the thickness of the boundary layer and is borne out by the experiments. The low-frequency noise level increases with the distance from the head of the buoyant unit. The high- frequency noise level, on the other hand, is considerably weaker at the rear of the buoyant unit where the boundary layer is very thick. The boundary layer of the buoyant units or of a vehicle of a similar shape is very thin at its head. For a buoyant unit the thickness is about a thousandth of an inch. The flow is there- fore laminar. The turbulence starts when the head merges into the cylindrical section. The noise that is received at a stagnation point is entirely due to the sound radiated from the turbulent zones into this area and to the eddies shed by the surface roughnesses. If the head of the unit is not highly polished, then the flow velocities become large enough an inch or two from the stagnation point, and the surface roughnesses generate eddies. Because of the laminar nature of the boundary layer in this part of the unit, the eddies decay very rapidly, but they do generate flow noise. This can easily be tested by performing measure- ments with hydrophones of different sizes. The received flow noise depends on the size of the hydrophone and consequently is at least partially nearfield noise. The flow becomes turbulent at the minimum pressure point which is very near to the joint between the cylindrical sectionand the head of the unit. In this region the velocities are 50% larger than the velocity of the vehicle and the turbulence is still very unstable and bumpy. The noise levels are therefore considerably larger than those which would correspond to the stable turbulence of the bound- ary layer. The region near this joint is particularly critical for the generation of flow noise. Toward the rear, one to two yards away from this joint, the tur- bulence has already decreased to its normal value and the noise level is approxi- mately the same as the noise level in the test section of the water tunnel. 270 Lecture 14 50- eS 5. 6) 9(-) 8 (---) i) 7 (===) \ / EO pee SSS. 6 (—) a SSE EXTERNAL NOISE ACCELEROMETER NUMBERED CURVES CORRESPOND TO READINGS FROM BUOYANT-UNIT HYDROPHONES LOCATED AS SHOWN IN ILLUSTRATION x ~ ACCELEROMETER DECIBEL SPECTRAL LEVEL (dbs) {e) ae (dbs, relative to gravity) EN EXTERNAL NOISE _ SHELL PRESSURE LEVEL =e) CONDITIONS OF MEASUREMENT Ss VELOCITY — 66 FPS NX -40 DEPTH — 200 FT 0.1 | 10 100 FREQUENCY (kc) Fig. 14.8. Flow-noise spectrum of buoyant unit when covered with grit. 6 50 @ 40 2 9 Sj) 30 F W > ye NUMBERED CURVES CORRESPOND zi TO READINGS FROM BUOYANT-UNIT a ; HYDROPHONES LOCATED AS SHOWN = . ‘ IN ILLUSTRATION () 10) ~ Ww a % 10 ) WwW @ -20 6 os CONDITIONS OF MEASUREMENT fa) \.8 -30 VELOCITY — 66 FPS Oe DEPTH — 200 FT 100 10 FREQUENCY (kc) Fig. 14.9, Flow-noise spectrum of buoyant unit with highly polished finish and waxed joints. E. J. Skudrzyk and G. P. Haddle 271 Figure 14.10 shows the noise spectrum recorded at hydrophone 8, located at the rear end of the cylindrical section. The boundary layer there is much thicker and the noise level is, therefore, more intense at the flow frequencies, as predicted by the theory. Conversely, the high-frequency noise levels are correspondingly lower. The curves for the polished surface, for instance, slope down very steeply (20 db per frequency-doubling). The readings obtained with hydrophone 8 were practically the same as those obtained with hydrophone 10, located just beyond the rear of the cylindrical section; therefore, only a limited number of readings was taken with hydrophone 10. Not filling the joint between the nose and the cylindrical section increases the low-frequency noise level recorded by the nose-section hydrophones by as much as 20 db and also increases the vibration level of the shell. Uncovered joints apparently generate larger eddies and, consequently, considerable low- frequency noise (Strouhal noise, for instance). But these large eddies also seem to increase the effective thickness of the boundary layer and reduce the gradients near the wall, lowering the high-frequency noise level considerably. The large eddies produced by the unwaxed joints apparently absorb a considerable fraction of the energy that otherwise would be available for the excitation of the high- frequency noise spectrum. Figure 14.11 summarizes the effects of various surface finishes (high polish, spray paint, fine grit, and coarse grit) at low frequencies (frequency range of 700 cps to 1.5 kc) and at high frequencies (frequency range of 20 to 40 kc). Grit can be seen to reduce the low-frequency noise level by as much as 10 to 16 db. Grit seems to have the effect of splitting up the larger eddies into smaller ones 56 ee aay 4 w oO Z I) fe) Ss NUMBERED CURVES CORRESPOND \ TO READINGS FROM BUOYANT -UNIT Ay HYDROPHONES LOCATED AS SHOWN IN ILLUSTRATION 3 DECIBEL SPECTRAL LEVEL (dbs) fe) \\ HIGH POLISH, UNWAXED yoInTs*X——\ -30 CONDITIONS OF MEASUREMENT \ SAN —40 VELOCITY - 55 FPS DEPTH — 200 FT a —50 CORRECTED FOR SPEED 0.1 ! 10 100 FREQUENCY (kc) Fig. 14.10. Flow noise measured by hydrophone No. 8 on the buoyant unit for various finishes. 272 Lecture 14 60- HYDROPHONE NO.6 HYDROPHONE NO.7 HYDROPHONE NO.9 |HYDROPHONE NO.8 (stagnation) (45 deg) (side) (rear) 50} Oo 40 te 30} *\ * 2o- x«\ * ia a 10 ee LOOMO MOO OMG DECIBEL SPECTRAL LEVEL (dbs) b w De) fe} (e) (e) ' oO {e) 2870 32 KC | fon) fe) | 2 3 4 | 2 3 4 | 2 3 4 | 2 Se DEGREE OF SURFACE ROUGHNESS CODE. | POLISHED 4 NO 24 GRIT 2 SPRAY PAINT GO POINT OF MEASUREMENT, JOINTS UNWAXED 3 NO. 120 GRIT * POINT OF MEASUREMENT, JOINTS WAXED Fig. 14.11. Comparison of flow noise for various degrees of surface roughness at high and low frequencies. and increasing the high-frequency noise spectrum, at least to some extent, at the expense of the low-frequency spectrum. At high frequencies the nose hydro- phone (No. 6) is particularly sensitive to surface roughness, and a high polish gives much better results than spray paint. The flow velocity at the circum- ference of the nose hydrophone is about 2 ft/sec. The Reynolds number obtained by the height of the roughnesses (0.001 in.) and the velocity that would be expected at the edges of the hydrophone is 25 and, hence, five times larger than the values required for shedding eddies. This Reynolds number would correspond to a noise level of roughly —60 db (re 1 d/cm’), as could be concluded from the rotating-cylinder measurements. Hydrophone 7, the 45° hydrophone, is not very sensitive to very small surface roughnesses over its area; the noise level is mostly radiated noise which masks the noise that would be produced by small surface roughnesses. However, the noise generated by coarser roughnesses over the hydrophone area seems to mask the radiated noise completely. At hy - drophone 8, on the other hand, the boundary layer is already relatively thick, and, as a consequence, the high-frequency boundary-layer noise is very weak. Therefore, most of the high-frequency noise observed at this hydrophone is due to the surface roughness, and polishing leads to much better results than the spray-paint finish. E. J. Skudrzyk and G. P. Haddle 273 14.7. RADIATED PRESSURE AND SHELL VIBRATION LEVEL A large hydrophone has been shown to be very insensitive (by a factor of "h 000 or more) to the small-scale turbulence that generates the high-frequency noise. Such a hydrophone measures essentially only those pressure fluctuations that are correlated over greater distances, such as the true sound pressure produced by the generation and decay of the eddies in the turbulent boundary layer. The hydrophone gives an indication of the true radiation field only; the validity of this indication has already been verified by the rotating-cylinder ex- periment and, again, by all the buoyant-unit runs, where the pressure inside the boundary layer, and outside at distances of about 100 yards from the buoyant unit, has been recorded. At the higher frequencies, the external pressure, when corrected for the geometrical decrease of its amplitude with distance, is prac- tically the same as the pressure recorded inside the boundary layer. The radi- ated pressure is usually greater than that which would be deduced from the vibration amplitude of the shell even under the most favorable conditions (as - suming pe as the value of the radiation resistance for the shell vibrations; see Fig. 14.8, double-dot-dash curve). In the frequency range of the measurements, the bending wavelength of the shell is always smaller than the sound wavelength. The very-large-scale pres- sure fluctuations that are responsible forthetrue sound radiation are, therefore, alternately in phase and out of phase with the bending modes of the shell and do not excite these modes very much. (A bending mode can be excited only if the pressure pattern shows variations similar to the mode function.) 14.8. EFFECT GF SIZE AND SHAPE OF HYDROPHONE ON THE RECEIVED NOISE LEVEL It has been shown above that the level of the nearfield flow noise that is picked up by a hydrophone greatly depends on the size of the hydrophone. How- ever, the experimental results show that this phenomenon is considerably more complex than was assumed initially. No area effect was found at the very low frequencies in the test section of the water tunnel; all the hydrophones were equally sensitive to flow noise in the frequency range 50 to 600 cps. This un- expected result leads to the conclusion that the correlation of the flow, in the test section of the water tunnel, in the transverse direction, is considerably greater than the boundary-layer thickness. That this conclusion is reasonable can be illustrated by smoke photographs of the turbulence around an airplane wing. Such photographs show that the turbulence is stratified in the direction transverse to the flow and that it is, therefore, correlated over great distances in this direction. The stratification seems to be particularly pronounced near the leading edge of the wing, where the turbulence is generated first, and is less pronounced toward the rear. At the frequencies above 1 kc, the area effect was very pronounced in the measurements in the water tunnel, whenever the hydrophone diameter was not very much largerthanthe boundary-layer thickness (see Fig. 14.5). A very pronounced area effect was also found for the rotating- cylinder measurements. At a frequency of 20 kc, a 5-in.-diameter hydrophone was 12 db less sensitive to flow noise than a 2,5-in.-diameter hydrophone. The noise level outside the boundary layer of the cylinder (3 ft distant from it) was 274 Lecture 14 r AREA EFFECT I7 IN. AFT soll A + ——— 1/8-IN.-DIA CIRCLE B x ———- I/4-IN.-DIA CIRCLE Aol ese C © ------- 1/2-IN.-DIA CIRCLE Bee D G —--— |-IN-DIA CIRCLE E 2-IN-DIA CIRCLE DBS (re! dyne) 20 L} a oO | S {e) ' a oO 0.1 | 10 100 FREQUENCY (kc) Fig. 14.12, Hydrophone-area effect on buoyant unit. about the same as that recorded inside withthe larger hydrophone. It was there- fore concluded that the area effect occurred whenever the hydrophone diameter was smaller than 5 in. The buoyant units exhibit the theoretical area effect at the very low and middle frequencies up to about 20 ke for hydrophones of, at the most, 1/, in.-diameter (see Fig. 14.12). Atthe higher frequencies the recorded noise seems to be essentially radiation-field noise and the recorded noise is therefore practically independent of the diameter of the hydrophone. The area effect is greatly dependent on the ratio of the diameter of the hy- drophone to the boundary-layer thickness and vanishes whenever the hydrophone becomes large. In contrast, the shape effect seems to persist irrespective of the hydrophone size. A rectangular hydrophone turns out to be particularly flow-noise sensitive, whereas a circular hydrophone is much less sensitive. Figure 14.13 illustrates this for a cylindrical hydrophone, which is similar in its behavior to a rectan- gular hydrophone. A fish-shaped hydrophone indicates a small noise level if the head of the fish points in the direction of the flow, and the noise level is 15 db larger if the fish points transverse to the main flow (Fig. 14.14a). The square shape shows a similar result when the corner is pointed in the direction of the flow (Fig. 14.14b). At frequencies above 8 kc, the nearfield sensitivity of most of the hydrophones used in the experiments became so poor that they indicated almost nothing but radiation-field noise (Fig. 14.14c). As a consequence, area and shape effects vanish. E. J. Skudrzyk and G. P. Haddle 275 ee) THEORETICAL SLOPE FOR RECTANGULAR OR CYLINDRICAL HYDROPHONE 40 -20 -40 DECIBEL SPECTRAL LEVEL (dbs) THEORETICAL SLOPE FOR PERFECTLY -60I— SHADED HYDROPHONE -80 0.01 0.1 | 10 FREQUENCY (kc) Fig. 14.13, Hydrophone-shape effect, 14.9. THE REDUCTION OF FLOW NOISE The flow-noise level depends greatly on the position of the hydrophone. The intensity of the low frequencies is relatively small at the front of the unit where the boundary layer is laminar, or turbulent and very thin. The high-frequency noise is very weak in the stagnation region, which is nonturbulent, and even weaker towards the rear of the unit where the boundary layer is very thick. The high-frequency level (above 15 kc) received by the head hydrophone can be re- duced considerably by the use of a flat head instead of a hemispherical head. Most of the noise that is received by this hydrophone is generated near the joint between the cylindrical section and the head. A flat head increases the shadow effect, and less noise is diffracted into the stagnation region. Turbulence- suppressing varnishes proved effective as noise reducers. A vaseline coating, for instance, reduced the noise level above 3 kc by almost 20 db. The noise level also depends greatly on the condition of the joint between the head and the cylindrical portion. If this joint is not filledin, the boundary layer becomes thick, as if it were tripped, or oscillates. Not filling in the joint reduces the high- frequency noise level but increases the low-frequency noise level. Methods are being examined that may lead to a further reduction in the noise level. 276 DBS (re | dyne) DBS (re | dyne) Lecture 14 SHAPE EFFECT I7 IN. AFT 50 H 0-() FLOW DIRECTION —> J +-< -20 (eee ee eee ggg a ee EE oH] | iKe) 100 FREQUENCY (kc) FIG. 14.14A SHAPE EFFECT 17 IN. AFT FO FLOW DIRECTION —> GO HYDROPHONES ARE I-IN. SQUARES O:l | 10 100 FREQUENCY (kc) FIG. 14.148 E. J. Skudrzyk and G. P. Haddle 277 epee ee SHAPE EFFECT 17 IN. AFT “a Do I-IN.-DIA DISK 5° a ~ FlOW Rs F go ——— I-IN.-SQUARE SSS pone SS page? eS ae — 86 r~ Sa . \ DIRECTION GO I-IN.- SQUARE ES J © —-— FISH, |.4-IN. LENGTH, 0.6-IN. WIDTH DBS (re! dyne) 0.1 | 10 100 FREQUENCY (kc) FIG. 14.14C Fig. 14.14. Hydrophone-shape effect. 14.10. THE REPRODUCIBILITY OF THE MEASUREMENTS AND THE EFFECT OF SHELL VIBRA- TIONS ON THE RESULT The results were obtained on different days and normally did not vary by more than two or three decibels. There were times when greater discrepancies were observed, however—discrepancies that could usually be attributed to tem- perature discontinuities or to great changes in the temperature structure of the sea. Some of the more important buoyant-unit runs were repeated five times; two runs were reserved for the recording of the low and middle frequencies and the remainder for the middle and high frequencies. Thus, five different record- ings of the middle frequencies (1 kc to 20 kc) were available to check the accuracy of the recordings. The measurements were not affected by shell vibrations. The driving-point impedance of the shell was about the same as the impedance of a 5-g mass at 1000 cps. The hydrophones had a mass of 800 g. Therefore, only "A 60 of the shell amplitude was transmitted to the hydrophones. This conclusion is in agreement with the experimental results obtained when the shell was driven in air with the same amplitude that normally would have been excited by the flow noise. The hydrophone readings were more than 40 db below the readings that would have been obtained if the shell had been excited by flow noise. In a second investi- gation, a heavy damping layer was applied to the shell, but the damping had no effect on the hydrophone responses. 278 Lecture 14 REF ERENCES . H. Schlichting, Boundary Layer Theory (McGraw-Hill Book Co., 1955). . J. Laufer, "Investigation of Turbulent Flow in a Two-Dimensional Channel," NACA Report V, 1053 (1951). . T. Theodorsen and A. Regier, "Experiments on Drag of Revolving Disks, Cylinders, and Streamline Rods at High Speeds,” NACA Report No. 793 (1945), .G.R. Batchelor, The Theory of Homogeneous Turbulence (Cambridge Univ. Press, New York, 1956). . R.H. Kraichnan, "Pressure Field Within Homogeneous Anisotropic Turbulence,” J. Acoust. Soc. Am., Vol. 28, 64-72 (1956); "Pressure Fluctuations in Turbulent Flow over a Flat Plate,” J. Acoust. Soc. Am., Vol. 28, 378-390 (1956). . V. A. Sandborn and W.H. Braun, "Turbulent Shear Spectra and Local Isotropy in the Low Speed Boundary Layer,” NACA TN 3761 (September, 1956). . V.A. Sandborn and R. J. Slogar, "Longitudinal Turbulent Spectrum Survey of Boundary Layers in Ad- verse Pressure Gradients,” NACA TN 3453 (May, 1955). . A.N. Kolmogorov, "The Local Structure of Turbulence in Incompressible Viscous Fluid for Large Reynolds Numbers,” C.R. Acad., Sci., Vol. 30, 301, U.R.S.S. 9. W. Heisenberg, "Zur statistischen Theorie der Turbulenz,” Z. angew. Phys., Vol. 124, 628-657 (1948). . Mark Harrison, J. Acoust. Soc. Am., Vol. 29, 1252A (1957); also appeared in full as Hydromechanics Laboratory Research and Development Report 1260 (December, 1958), Dept. of the Navy, David Taylor Model Basin. . W.W. Willmarth, "Space—Time Correlations and Spectra of Wall Pressure in a Turbulent Boundary Layer,” NASA Memorandum 3-17-59W (March, 1959). . E. J. Skudrzyk and G. P. Haddle, "Noise Production in a Turbulent Boundary Layer by Smooth and Rough Surfaces,” J. Acoust. Soc. Am., Vol. 32, 19-34 (January, 1960). . M. J. Lighthill, "On Sound Generated Aerodynamically,” Part I, Proc. Roy. Soc. (London) A, Vol. 211, 564 (1952); Part II, Vol. 221, 1 (1954). . I. Proudman, "The Generation of Noise by Isotropic Turbulence,” Proc. Roy. Soc. (London) A, Vol. 214, 119-132 (1952). . G.M. Corcos, J.W. Cuthbert, and W.A. Von Winkle, "On the Measurement of Turbulent Pressure Fluctuations with a Transducer of Finite Size,” Univ. Calif., Ser. No. 82, Contract No. N-oar-222(30), (November, 1959). 16. M. Goldstein, "A Note of Roughness,” A.R.U., Report and Memo No. 1763 (1936). . L.N. Wilson, "Experimental Investigation of the Noise Generated by the Turbulent Flow around a Ro- tating Cylinder,” J. Acoust. Soc. Am., Vol. 32, 1203-1207 (October, 1960). LECTURE 15 SOME CONTRIBUTIONS FROM AERONAUTICS TO THE FIELD OF UNDERWATER NOISE E.J. Richards, J. L. Willis, and D.J.M. Williams Department of Aeronautics and Astronautics University of Southampton Southampton, England 15.1. INTRODUCTION During the last fifteen years, the introduction of jet engines into civil aircraft operation has accentuated the problem of noise in aviation, and many investiga - tions have been made which are of distinct significance in the apparently distant field of underwater noise. For example, withthe growth of aircraft engine power, the speeds of aircraft have increased to such a degree that the rough boundary flow along the fuselage gives rise to the majority of the noise inside the cabin; it gives rise to fuselage vibrations which can in certain circumstances cause skin cracks and fuselage and wing failures, and it is suspected that the radiated noise from the fuselage movement may have some effect on transition from laminar flow on neighboring surfaces. The noise radiated from such fuselages is very much a function of the modes of oscillation and the degree of damping, both structural and acoustic, involved in these particular modes. In the field of engine design also, such problems arise. It is known that compressor noise has a large random content which is related to the boundary-layer pressure fluctua - tions on the blades and is caused by the unsteadiness of the flow incident upon them. This problem of noise radiated from blades is now arousing major interest in engine design. The knowledge gained from investigation of these various factors is often directly applicable to analogous problems in underwater noise. For instance, the problem of the boundary-layer noise radiated from the hull of a vessel is closely related to that of radiation from a fuselage boundary layer; the effects of pressure gradients, waviness, rivets, roughness, skin discontinuities, and so on, have their obvious equivalents. Similarly, the skin response to boundary-layer pressure fluctuations has an exact analogy in the self-noise within an Asdic dome, and in the structural vibration of a submarine. Still further, the use of correlation techniques and fuselage damping to identify and supress fuselage vibrations must also be of interest to naval personnel seeking to reduce the reradiation of noise from their craft. 279 280 Lecture 15 It is impossible to describe here all the investigations of interest to naval research workers. Therefore discussion will be confined to three aspects of our work at Southampton University, viz: 1. The nature of boundary-layer pressure fluctuations and the effect of single roughnesses 2. The radiated sound from a small flat plate 3. The modes of oscillation of structures, the acoustic damping achieved, and the reradiated noise problem In addition, the significance of the investigations to the field of underwater noise will be illustrated by some simple calculations of radiated and self- noise based on the above and other investigations. 15,2, BOUNDARY-LAYER PRESSURE FLUCTUATIONS We are interested in measuring the pressure fluctuations on the surface of an aircraft both at subsonic and supersonic speeds in order to ascertain the fluctu- ating loads occurring on it and in order to obtain the information necessary to calculate the noise radiated from the surface as a result of these fluctuating forces. It has been necessary to measure not only the rms pressure at the skin, but also the areas over which these pressures are correlated and the power spectrum of the fluctuating pressures relativetoaconvected frame of reference. Fig. 15.1. Boundary-layer wind tunnel. E. J. Richards, J. L. Willis, and D. J. M. Williams 281 Two experimental rigs have been used to do this; these are shown in Figs. 15.1 and 15.2. Figure 15.1 shows an induced-flow airchannel of massive construction incorporating two measurement areas, one subsonic, the other supersonic. The supersonic region acts incidentally as a choke to prevent the radiation of any injector noise forward into the subsonic working section and results in a low level of background noise against which the boundary-layer pressure fluctuations are measured. Some difficulties have arisen, however, in eliminating low- frequency vibration [1] and, consequently, the results are tentative in this frequency region. The second facility (Fig. 15.2) is a water rig. Water flows vertically from an overhead tank via a series of gauzes and a well-designed contraction and into a base tank. The header tank andthe pipe are isolated from any outside vibrations of the building. The elimination of background machinery noise by the use of a gravity feed has proved to be useful andmeasurements may be made in boundary layers of up to one inch in thickness. Again, some low-frequency vibration occurred, but much of this has been traced to a vibration of the pipe and has been reduced by the addition of a damping material to the outside of the pipe. Even so, it is suspected that some acoustical interference at frequencies of 200 Fig. 15.2. The water rig. 282 Lecture 15 Fig. 15.3. Transducer bank. 8 u 0) 6 x A © z © % 4 o Py © WILLIS [F © WILLIAMS 2 X BULL 4 WILLMARTH 5 10 15 2-0 Mach number (Free stream) Fig, 15.4. Over-all rms pressures. cps and below occurs, and this aspect is being further investigated. In view of the smallness of the pipe and our interest in pressure fluctuations at a point rather thanthe fluctuating loads over an area, Willis [2] at Southampton developed extremely small lead—zirconate—titanate pressure transducérs in a bank of twenty or more (Fig. 15.3) to determine the relative properties of the pressures at neighboring points. Figure 15.4 indicates the over-all pressure levels obtained in the various experiments. It is seen that both Willis [2] and Bull [1] agree very well with the E. J. Richards, J. L. Willis, and D. J. M. Williams 283 © WILLS (Water) © WILLIAMS 002 +004 006 008 ™ 2 SEie/aipu Fig. 15.5. Over-all rms pressures. smooth-flow over-all rms pressure level of 0.006q* obtained by Willmarth [3], while Williams [4] in his experiments at low supersonic speeds has pressure fluctuations at the walls which fall with forward Mach number but which are in general agreement with the low subsonic answers. If, as is more logical, the pressure fluctuations are plotted against the local skin friction at the walls, we get a level of 37, Tin the subsonic work, and a variation between 2.47, and 1.279 in Williams' supersonic investigations; see Fig. 15.5. To evaluate the spectral content ofthese pressure fluctuations, it is necessary to bear in mind the purpose for which these spectra are to be used. If they are to be incorporated into structural-response calculations, the normal spectral measurement methods are satisfactory; if, however, it is necessary to calculate the radiated noise from the pressure fluctuations at the surface, it is usual to carry out the calculations in terms of turbulence being convected along the surface with some mean speed of flow of the turbulence. Thus, the significant spectra are those of turbulence as seen by an observer moving along the surface with the mean velocity of convection, not those at a stationary point. Such spectra * ais the mean flow in the dynamic head. t7ois the wall shearing stress or skin friction. 284 Lecture 15 09 *suoljenion{y ainssoaad [JBM Jo SAA.MD uoTe{e1I0D-Sso1D *g°ST “BI Sul 690-=x9 dasfsur 90¢ =°N E. J. Richards, J. L. Willis, and D. J. M. Williams 285 can be obtained using space—time correlation methods; the curves of Fig. 15.6 indicate typical results obtained by Willis and Bull in their work for various transducer spacings. The optimum convection speed can be obtained from the delay time giving the best correlation for the various spacings, or from the time delay for envelope tangency; the results differ very little. Figure 15.7 shows the convection speed based on different separations ofthe microphones. The variation of velocity so obtained is significant, indicating, as would be expected, that the large eddies in the boundary layer are convected at higher speeds than the smaller eddies. The convection speed of interest is clearly that of the noise- radiating eddies (i.e., the highest frequency at which the energy level is high). The fixed and moving frame spectra of pressure fluctuations can be obtained from the cross-correlation curves, the Fourier cosinetransform of the envelope to the fixed-point cross-correlation curves giving the moving-frame power spectra. Figure 15.8 indicates these two spectra and the essential differences between them also shown, but to an arbitrary scale, is the spectrum of the pressure—time derivative op/dt, a parameter directly related to the radiated noise from the wall pressure fluctuations [17]. In aviation, these pressure fluctuations are modified in many ways by the specific environment of the flow. For example, in separated flow over a narrow delta wing, Jones and Judd [5] have shownthat wing pressure fluctuations beneath the cast-off vortex are increased some tenfold and are well correlated over quite large areas of the wing. Thus, the noise radiated in such instances is presumably far greater than that calculated from normal turbulent boundary layers. Other, though smaller, increases occur, however, behind discontinuities in the surface or in regions of roughness, and these are presently being studied at Southampton [2]. For example, the variation of rms pressure behind a rectangular ridge of ‘/,-in. length and 0.1-in. height in a boundary-layer flow is shown in Fig. 15.9. It is seen that the rms pressure increases with distance behind the ridge to a value r) 4 8 12 16 20 7 Fig. 15.7. Variation of convection velocity with distance along the tunnel wall. 286 Lecture 15 twice that of the smooth-flow condition and ceases to have an effect some 20 heights downstream. Further studies of the detailed effects of discontinuities, roughness, pressure zradients, and waviness of surface are proceeding at Southampton and will be reported later. The work is clearly of great interest in a wide variety of contexts as will be shown later by an elementary attempt to illustrate the significance of these results. 15.2.1. The Radiated Sound from a Small Flat Plate It is difficult to check the theory of radiated noise from these pressure fluctuations since it is impossible to place a microphone, shielded from the flow, Fig. 15.8. Comparison of spectra of pressure fluctuation on the wall adjacent to a turbulent boundary layer. Curves: (1) fixedaxis, (2) moving axis, (3) moving axis + 6 db/octave (arbitrary ordinate scale), within the restricted space of a wind-tunnel working section and also in the far field in which reactive effects are absent. Some attempts, however, have been made at Southampton to obtain the radiation from flat plates in jet flows. The agreement between the measured and predicted far-field noise [6], which is quite good, justifies the use of existing theory in the prediction of radiated noise from a boundary layer. The only reference necessary atthis point is to the directional pattern to be obtained. Figure 15.10 shows a plot of the noise variation circum- ferentially around a small aerofoil placed at zero incidence in a jet compared with the theoretical pattern obtained from a single dipole with its axis at right angles to the surface. Since the noise radiated along the surface is theoretically zero for this type of wall pressure radiation, we cannot obtain any true indica- tion of the noise radiated along the surface without introducing theories of scatter and diffraction. With present knowledge, therefore, the best method of calculating E. J. Richards, J. L. Willis, and D. J. M. Williams 287 25 A400 - ae 300; aN / 2 aca cane. ie Ss 6B PRESSURE GRADIENT (Lo/exy, =) A (Peonsr - Peranc) Lejs 4 (ins) DISTANCE BEHINO STEP Fig. 15.9. Measurements taken behind 0.10-in. step. the noise radiated from one part of a body to another is to relate it to the theoretical total acoustic power output, modified to allow empirically for the directional pattern as, for example, obtained in Fig. 15.10. Thus, some idea of the noise environment of a laminar region of a wing produced by the radiated noise from the turbulent region downstream can be obtained from the theoretically computed total acoustic output reduced by some 6 db (see Fig. 15.10) to allow for the directionality of the sound field. This distribution of the sound field is of course a function of the boundary-layer thickness, but this may not introduce a great error since the frequency at which the wall pressure fluctuations fall off (and therefore the frequency of greatest noise emission) is also related to the boundary-layer thickness. 15.3, STRUCTURAL RESPONSE AND RERADIATION A structure as complicated as that of an airplane or submarine has a large number of possible modes of vibration, all of which can conceivably be excited in any particular case. Clarkson, however, has indicated by careful cross- correlation techniques that at least in the Caravelle [7] and the Comet [8] the number of modes excited by jet noise is quite small and manageable. For example, Fig. 15.11 shows the root-mean-square stress level in one plane of the Caravelle while Fig. 15.12 shows the cross correlation at each frequency 288 —— —-— Theoretical dipole Measured g = 150 Ibs/fr? Measured at aerofoil position Flat plate \" chord Fig. 15.10. Polar plot of noise from small flat-plate aerofoil at zero incidence measured at three-foot radius. between the stresses in two adjacent panels aroundthe periphery of the fuselage. In this case, at least, the actual motion is independent between frames but takes on an approximate "hourglass" or "“eggtimer" mode around the periphery, adjacent panels being antiphase. The reradiation from such a motion can be calculated and the acoustic damping of such an array estimated. Calculations have been carried out by Mead [9] of the acoustic damping ratio of flat, rectangular, simply supported panels of various length-to-breadth ratios, mounted in a rigid structure and vibrating in their fundamental modes (see Fig. 15.13). The reradiation is simply calcu- lated in such cases and can be used to indicate the noise radiated once the panel movements are known. Preliminary tests on the acoustic damping of arrays of panels have com- menced at Southampton [10] by testing a single panel as shown in Fig. 15.14. As shown in Fig. 15.13, the agreement with theory in this particular case is good. E. J. Richards, J. L. Willis, and D. J. M. Williams 289 PoweR SPECTRAK BENSITY (ARBITRARY Scale) 200 hao Goo Bao 1a09 Feeavency ( 7 ss ib J Ww? Hy v ay, de et \y P ¥ ’ eke A Bi yeas ¥ i i f i i LECTURE 16 UNDERWATER ACOUSTICS AS A TOOL IN OCEANOGRAPHY M.J. Tucker and A.R. Stubbs National Institute of Oceanography Wormley, Surrey England 16.1. INTRODUCTION Electromagnetic waves are severely attenuated in sea water, but fortunately sound travels well enough to be used for many of the purposes served by radio and radar in the atmosphere. Historically, the principle was first applied to find the depth of the sea; a sound impulse was made in the water and the time it took for the echo from the sea bed to return to the ship was measured. As techniques for this "echo-sounding" were developed, it became apparent that echoes were also being obtained from objects in midwater. These turned out to be fish shoals, and nowadays no fishing boat of any size would put to sea without an echo-sounder for locating fish. Probably the most important scientific application has been the examination of the geology of the sea bed. In suitable areas it has been possible to determine the geological structure of the sea floor in more detail than is possible in many land areas, and much useful information is being obtained about the transport of sediments. In the realm of biology, the habits of fish shoals have been determined using a scanning asdic to follow their movements, and something has been learned about the habits and composition of plankton. This is a fascinating field in which acoustics should be a powerful tool, but the application is still in its infancy. The telemetering of information using the acoustic wave as a carrier is also in its infancy, but is potentially of wide application. 16.2. MARINE GEOLOGICAL APPLICATIONS 16.2.1. Precision Echo-Sounding The method of measuring the depth of the sea by transmitting a pulse of sound from the ship and measuring the echo-time is well known. In the last few years, major improvements in the technique of echo-sounding in the deep sea have been made, notably at the Woods Hole Oceanographic Institution [1] and at the Lamont Geological Observatory, and it is now possible to measure depths of 3000 fathoms or more to an accuracy of one fathom in any weather in which 301 302 Lecture 16 TIME (sec) \ 2 3 4 5 6 7 8 9 10 7 12 Transmission Fegiage RN Sroa ts Dovates Saba mic Receiver ee OFF ON Echoes s t i 4 f 4 = ee RECORDED Fig. 16.1. Coding system of the precision echo-sounder. The diagram is drawn for an echo from ap- proximately 1300 fathoms. the ship can operate. In the recording system used, the stylus records continu- ously, so there is no chance of missing a bottom echo because the stylus is on the wrong phase. Precision has been obtained by using a precision timed recorder with an open scale. Since these recorders are used in many oceanographic instruments, including two to be discussed below, they will be described here in some detail. They are usually modified facsimile picture receivers; the ones used by N.I.O. and described here are part ofthe Mufaxsystem. The stylus consists of a single- turn helical blade rotating against a knife edge with chemically impregnated paper in between. The point of contact between the helix and the blade starts at one edge of the chart, moves across to the other edge, and then immediately enters at the first edge again, so that it is always on the chart. Passage of cur- rent between the helix and the stylus dissolves some iron from the stylus which reacts with the chemicals in the damp paper to form a black mark. The helix is driven by a synchronous motor supplied from a tuning fork, so that its rate of rotation is precisely controlled. The usual speed is one revolution per second. A contact on the helix shaft closes as the writing point moves onto one side of the chart and initiates the transmission of the acoustic pulse into the water. a ECE, Waters ane echo from eae sea 1 Issel may not return ae after Save rear apecryeen rereeeerepeernpsnsennayy erry hia ; " ai ci nn a I sn nn i" H HU a rh A nT | A m1 I TET Mac Ms aan ian or comer | uM POE AN ca i on i AA: al ii A NN GA ee i at i AA AAA A | il | ic ies on | i AA Fl | Fig. 16.2. A typical nO a taken with the precision echo-sounder. M. J. Tucker and A. R. Stubbs 303 revolutions of the helix, and if no precautions were taken might well be lost in the transmission mark or in the reverberation due to scatterers in midwater. To overcome these difficulties and to find out how many complete revolutions of the helix elapse before the echo returns, a switching system is used. Figure 16.1 shows a typical arrangement using twelve sweeps of the helix. Pulses are transmitted on only the first six and the receiver is switched off for the first four sweeps. Thus, apart from the fifth and sixth sweep, there is negligible local reverberation and the number of echoes received allows the number of revolu- tions between transmission and echo to be determined. This number is usually determined by ear, as successive sweeps are not well separated on the record. To overcome errors due to shrinkage of the paper in drying, range marks are put on the paper by counting down the tuning-fork frequency to produce suit - fe Fig. 16.3. Part of a bathymetric chart of the Swallow Bank; area, approximately 30 by 35 miles. The depths are marked in fathoms. This figure shows the remarkable consistency which can be obtained using the precision echo-sounder, (Chart from A.S. Laughton.) 304 Lecture 16 ably spaced pulses which are superimposed on the echoes as shown in Fig. 16.2. The counters are reset by the transmission. Assuming a velocity of sound of 800 fathoms/sec, and with a helix rate of 1 rps, the chart width represents 400 fathoms and the position of the echo can be readily determined to the nearest fathom. Part of a chart produced froma precision echo-sounder survey is shown in Fig. 16.3 and demonstrates the remarkable consistency with which the depth can be measured. Among other things, the use of precision echo-sounders has enabled geolo- gists to understand much more about the sedimentation processes in the sea. Laughton [2], for example, has surveyed a channel between two abyssal plains, formed by the passage of turbidity currents. An old-fashioned echo-sounder could have given the precision to show the feeder channels and the general slope of the plain only if its timing were checked every few minutes. An echo-sounder using a transducer mounted on the hull of a ship usually fails even in moderately rough seas due to "blanketing" of the transducer by air bubbles dragged under the shipas she pitches. This has been overcome by mount - ing the transducer in a streamlined body towed on a short warp (typically 40 ft) from a boom alongside the ship. This arrangement will give satisfactory results in all weathers. 16.2.2. Multiple-Beam and Scanning Echo-Sounders To quote Professor Brackett Hersey, the conventional echo-sounder (even the precision echo-sounder!) is a blunt instrument. With a typical beam angle of 30°, it "illuminates" a large area of the sea floor and misses all the fine detail. To obtain narrower beam angles involves using large transducers and stabilizing them against the roll ofthe ship; but even if such a system is achieved, a large number of runs is required to survey an area in detail. Thought is being devoted to these problems and various systems have been tried, but none is really operational yet. Howson and Dunn [3], following suggestions by D.G. Tucker [4], have experi- mented with multiple-beam echo-sounders in which the beams are formed by an interferometer using two strip transducers, and also with high-speed electronic beam-scanning techniques. These enable a comparatively wide strip of sea floor to be surveyed on a single run. In the multiple-beam system, identification of the beams is a problem, since the records from all of them appear on the same chart; M. J. Tucker [5] has suggested that this can be overcome to some extent by tilting the transducer so that the pattern is unsymmetrical and port and star- board beams are distinguishable by their intensities. Figure 16.4 shows an ex- ample of a record taken with such asystem. The beams were very narrow in the fore-and-aft direction (1.3°) and separated by about 15° athwartships. The trans- ducer was tilted to the angle shown so that the central (most intense) beam pointed to starboard. This record shows that the bed of the small canyon crossed tilted downwards 2.5° from the horizontal in a direction of 110°T. The present difficulty with the electronic sector-scanning technique is that the sea-bed profile athwartships is presented on a CRO, and no means of making a permanent record has been devised except photography of the traces, which would not be satisfactory in practical use. The basic difficulty is, of course, that three dimensions have to be recorded. M. J. Tucker and A. R. Stubbs 305 TRANSMISSION ——> 100 FM — 200 FM —— 300FM —— _ TILT CHANGED TO 20° 1O MIN Fig. 16.4. Record from an echo-sounder employing multiple beams, From the record it can be shown that the bed of the canyon slopes at 2.5° in a direction of 110°T. 16.2.3. Echo-Sounding for Subbottom Strata Ordinary echo-sounders do not usually show reflections from strata below the sea bed. This is probably due mostly to the high attenuation of these fre- quencies in the sea-bed material, but is probably also due in part to the high reverberation level from irregularities in this material. Under very favorable conditions, 10-kcps sounders will penetrate at least 100 ft of mud to show the bedrock underneath (Fig. 16.5), and where they will do so they are most useful because they have higher resolution than the devices described below. In order to get deeper penetration, and in less favorable conditions, lower frequencies are necessary, since these show much less attenuation and reverberation. The use of these low frequencies presents major design problems. Firstly, the ambient noise level in the sea rises rapidly at low frequencies, as does also ship's noise, and high pulse powers of the order of 1 Mw are therefore required from the transmitter. Owing to the long wavelength, the number of waves in the transmitted pulse must be kept small if useful resolution is to be obtained. A half wave would be ideal, but this requires wide-band receivers, which again increase the noise level. Thetypes oftransducers used at supersonic frequencies are thus not suitable. 306 Lecture 16 s oi Ye ee Ae [ee 40 FMS, —————>| j}¢—_—_—___—— APPROX. 4 MILES —————————__>| Fig. 16.5. Ten-kcps echo-sounder record showing penetration of soft mud over bedrock, Several kinds of sound source have been designed for this application. The "Sonoprobe" developed by the Magnolia Oil Co. produces approximately a half wave of 3.8-kcps sound with a peak power of about 10 Mw. This is still rather a high frequency for deep penetration, but it has high resolution. Underwater sparks have been used with considerable success [6] but always produce a double pulse due to the collapse of the gas bubble, and this reduces their effective resolution. Perhaps the most interesting and promising device isthe Edgerton "Thumper" [7]. This is extremely simple in principle, consisting of a flat coil of wire with a circular aluminum plate 20 in. in diameter held loosely against it. A pulse of current passed through the coil produces a strong magnetic field which induces eddy currents in the aluminum plate. The interaction of these eddy currents with the magnetic field produces a force which strongly repels the plate from the coil, and thus produces an acoustic pulse in the water. The standard unit uses a peak current of about 2000 amp from the discharge of a 160- pf capacitor charged to about 4 kv and produces a peak pressure of about 250,000 d/em? at 1 yard. The initial pulse consists of aclean unidirectional pressure pulse lasting about 0.5 msec, but unfortunately this was followed in the original design by two or three waves of lower frequency caused by various factors. N.I.O. has made major modifications to the mounting arrangements of the coil and plate, and it seems that this has considerably improved the waveform, but at the time of writing the system is still being tested at sea, and the precise waveforms are not available. N.1I.0. is now using as a receiver a line array of hydrophones towed behind the ship so that the array has almost zero sensitivity in the forward direction and thus does not hear the noise generated by the ship. The received signal is passed through a band-pass filter with a range of 300 cps to 1 kcps, which has to be specially designed to have a good impulse response. Using this system towed at 7'/, knots, echoes trom strata arriving 0.16 sec after the bottom echo have been obtained in water depths of about 900 ft. We understand (private com- munication) that considerably better results have been obtained in the United M. J. Tucker and A. R. Stubbs 307 — TRANSMISSION — DIRECT PULSE —SEA FLOOR 70 FMS. -0-2 -0O3 — SECOND ECHO FROM SEA FLOOR —0'5 SECS. Se i Fig. 16.6. Record taken using the "Thumper." States using a more powerful Thumper. A typical record is shown in Fig. 16.6; this was obtained using the original Thumper and a nondirectional hydrophone. 16.2.4. Seismic Refraction Shooting When the very deep rocks below the sea bed are to be examined, a system known as seismic refraction shooting is used. The principle of this method is shown in Fig. 16.7. An explosive charge, which may vary from a ‘)-Ib charge to a depth charge, is set off nearthe ship, A. The sound travels by various paths to a number of sono-radio buoys which transmit the received sound back to the ship by radio. The travel time of the first sound to arrive at the receiver is plotted against the horizontal distance given by the travel time of the direct water wave to give a diagram as in Fig. 16.8. At close ranges, the first sound to arrive has traveled through the direct water path, but at longer ranges the higher velocity of sound in the sediment layer means that sound through this path arrives first. At even longer ranges, the shortest path is through the deeper but even higher velocity layers. Thus, the diagram consists of a series of straight lines, each representing a stratum, whose slopes give the velocity of sound in that stratum. From the intercepts with the axis, the depth of the stratum can be determined. Thus, not only the true depth, but also some clue as to the compo- sition of the stratum can be obtained, by comparing the observed velocities with those of known rocks. This technique can penetrate several miles below the sea bed. 16.2.5. Sea-Bed Survey Using Asdic Chesterman, Clynick, and Stride [8] provided the first published account relating certain bottom reverberation patterns on an asdic record to the sea-bed geology. The equipment in use at N.I.O. was designed primarily for fish-detection 308 Lecture 16 ke 6 to 20 miles —_—__»| Radio waves Water waves Hydroph ones Velocity V, | SUNN E ATCO 000000 reeneenecrernccen i Tl = MANTLE ROCK Velocity V4 inim Fig. 16.7. Principle of seismic refraction method showing different paths by which waves can travel from explosion to sono buoy. Distance Fig. 16.8. Graph of travel times against distance for seismic refraction shooting. M. J. Tucker and A. R. Stubbs 309 UPPER SIDE LOBES SEA SURFACE SEA BED Fig. 16.9. Diagram showing vertical arrangement of beams of the asdic mounted in the R.R.S. "Discovery II.” studies, but also with the geological application in mind, and has in practice become a most powerful geological tool. (See Tucker and Stubbs [9] for a detailed description of the instrument and Stride [10] fora survey of the geological uses.) The asdic points sideways from the ship, with a narrow beam of 1.3° in plan view and a wider beam in the vertical plane (approximately 11° in the usual ar- rangement). The main particulars are: ITESCWOMEY cao donc coboa0 do BO NCOs Pulse length..............0.3 to 3 msec (normally used at 1 msec) PUSS OWEIE 5 oo oo oo 000008 0 OW) Wy Repetition rate... -..... . 1 pulse perm sec Maximum recorder range... . . 800 PORE EMG | >) Wl =I = N x Oo a a a < the Fig. 16.10. Asdic record showing strata on the sea floor in Bristol Channel. 310 Lecture 16 The side lobes in the vertical plane are important (Fig. 16.9) and give useful information. Figure 16.10 shows a record taken with this equipment. Starting from the left-hand side of the record and referring also to Fig. 16.9, there is first the transmission mark (somewhat ragged because the blade has been eaten away at this point). Then comes a hard line which is the bottom echo from the vertical side lobe, followed closely by the echo from the third side lobe, then by those from the second and first side lobes, and finally the echoes from the main beam extending across the rest of the record. Figure 16.10 shows an area where the bottom has been largely swept clean of sediment and the bedrock is exposed. Figure 16.11 shows a sediment-covered area where sand waves have been formed. It will be seen that the side lobes give a quantitative measure ofthe bottom relief and aid in the interpretation of the acoustic picture. }¢—___________- ‘g00 yps_. ———______ >} |_<—____________ AppROx. 2 MILES Fig. 16.11. Asdic record showing sand waves in the Irish Sea. M. J. Tucker and A. R. Stubbs 311 It is advantageous to be able to alter the relative amplitude of the side lobes so that they produce recordings of roughly equal density, and for this purpose the transducer is divided into three horizontal strips whose relative sensitivities can be altered. The most satisfactory arrangement for geological survey work is to have the relative sensitivities in the ratio 3 to 2 to 3. High resolution in the recorder and good correlation between adjacent traces is required, so a Mufax recorder as described above is used. The transducer is stabilized against the roll ofthe ship; otherwise the side-lobe patterns become confused in rough weather. The instrument has given useful results in depths of up to 100 fathoms. 16.3. BIOLOGICAL APPLICATIONS 16.3.1. Fish Detection Although this subject comes under the field of fishery research rather than oceanography, a brief account of it should be of interest here. An echo-sounder of adequate sensitivity will show echoes from midwater organisms. The most powerful echoes come from shoais of fish, and the vast majority of the larger fishing boats nowadays are equipped with echo-sounders specially designed for finding fish shoals. One of the most difficult problems for the fisherman is to decide what kind of fish he is seeing. At present, this is largely a matter of experience and local knowledge. He knows that at a particular time of year in a particular position, a particular type of pattern on the recorder usually means a certain kind of fish. Even an experienced fisherman often makes mistakes, however, and will catch valueless fish; thus, there is much interest in finding some means of identifying the fish. Present ideas suggest either using high-resolution echo-sounders with narrow acoustic beams [11], which will show more detail of the structure of the shoal, or measuring the frequency dependence of the echo strength. This latter idea is attractive in principle, but presents severe practical problems which have not yet been overcome. A second problem which has been solved with a fair measure of success is the detection near the sea bed of fish which can be caught by bottom trawls. The vertical height of the opening of such a trawl is about 12 ft, and it is fish within this distance of the sea bed which have to be detected. Most important is cod, a fairly large fish with an acoustic cross section of up to about 1000 cm? at typical echo-sounding frequencies. Echo-sounders can be made which will detect even individual cod up to the maximum trawling depth (say, 300 fathoms), the difficulty being to obtain sufficient resolution to separate these echoes from the bottom echo. Currently, the system most commonly used is to present the echo trace on a cathode-ray oscilloscope using an "A scan," but with the time base expanded and its initiation controlled so that only the last 50 or 60 ft above the sea bed is presented (Fig. 16.12). This is, however, rather a trying display to watch, and systems have been developed to separate fish and sea-bed echoes on a paper recorder [12]. The area examined by an echo-sounder is, of course, a comparatively small lane directly beneath the path of the ship; thus, horizontal echo-rangers (asdics) are beginning to be used to look for fish over a wider area. There are several 312 Lecture 16 Fig. 16.12. Cod echoes displayed on Fish-lupe. Expanded portion of trace is about seven fathoms. models commercially available, ranging from a short-range, high-resolution instrument used by purse-seine fishermen to models with ranges up to 2000 yards. A record taken with the N.I.O. asdic described in Section 16.2.5 is shown in Fig. 16.13. It will be seen that fish close to the ship appear very clearly, but at longer ranges where the main beam hits the sea bed, the fish echoes have to compete with bottom reverberation and detection is more difficult. The long ranges of detection are only obtained where the sea bed is smooth and has com- paratively low reverberation. 16.3.2. Scattering Layers Apart from the dense shoals of fish, a sensitive echo-sounder also records reverberation from diffuse and more or less continuous layers in the sea. A narrow-beam, high-resolution sounder operating in deep water willusually show a complex structure of layers, some of which migrate to the surface at night and return to deeper water at dawn. A record taken with a narrow-beam sounder (the N.I.O. asdic turned with the beam axis vertical) is shown in Fig. 16.14. M. J. Tucker and A. R. Stubbs 313 800 YDS. TATTR Oy EE Tee | i i. 307 DPSS be] SaO es . : aS ul z =I t: =! § = 4, ; = 7 AS x a & as a Ld < ae Mb WA hy Ade eee Fig. 16.13. Asdic record showing large fish concentration in midwater. Surprisingly little is known about the composition of these layers. One can tow a plankton net through them and usually catch nothing which apparently could cause the level of reverberation actually observed. With the aid of acoustic techniques, it is sometimes possible to identify the organisms in one or two layers with a fair degree of certainty. In the record shown, for example, which was taken with a 36-kcps sounder, the diffuse layer between 250 and 350 fathoms did not appear on the record from a 16-kcps sounder. A net haul through this layer caught a number of small fish (Cyclothone sp.) 2 or 3 cm long, whose air bladders would resonate at a frequency in the region of 36 kcps; and though calculation showed that the number caught, compared with the volume swept out by the net, was hardly sufficient to cause the observed level of reverberation, it is known that active animalscanavoidthe net, and it seems reasonably certain that this layer was composed of these fish. We have occasionally managed to identify other layers by a similar technique, and Hersey [13] has managed to identify a scattering layer with some certainty using a more refined technique for measuring the frequency characteristics. From the acoustic results, it seems reasonably certain that the nets used at present by biologists are very inefficient for sampling certain types of or- ganisms in the sea, and we may well have a completely false idea of the relative abundance of the different species. 314 Lecture 16 APPROX 40 MINUTES. - Pe Fig. 16.14. Record from asdic equipment used as an echo-sounder showing migrating scattering layers. 16.4, ACOUSTIC TELEMETERING 16.4.1. General Compared with radio telemetering in the atmosphere, acoustic telemetering in the sea is in its earliest infancy. Marine scientists and engineers are con- stantly agitating for all kinds of telemetering devices: depth-of-net meters, devices for telemetering the behavior of dredges, telemetering temperature meters, and so on, but the number of people available in civilian establishments with the rather specialized knowledge necessary for the development of these devices is so small that progress is slow. It is perhaps relevant to ask way the information is not brought up via electric cables. Oil-well engineers, for example, lower equipment to similar depths in oil wells on strain-bearing cables incorporating one or more conductors, as a matter of routine. Oceanographers do in fact use similar cables, but they are not really satisfactory for several reasons. In many ways marine use is more severe than use in oil wells; in particular, because of the vertical motion of the point of suspension due to wave-induced pitching and rolling of the ship, and because of the extra strain, vibration, and twisting due to towing the cable through the water: even the normal drift of the ship or differential currents may be sig- nificant in this respect. Perhaps the difficulties can best be illustrated by considering a particular cable designed specifically for marine use by a specialist in the field. Briefly, M. J. Tucker and A. R. Stubbs 315 the specifications of this cable are: Over-all diameter...... 0.270 in. Weight in water........ 150 lb per 1000 yards Breakin oelOaG ey mueriaerene = 2500 Ib Resistance per core..... 40 ohms per 1000 yards An 8000-yard length would be required to operate gear near the bottom in deep water. The weight of the cable alone is half its breaking strain, which is not a good factor of safety, even with no equipment on the end. At a towing speed of one knot, the wire would stream out at an angle of about 45°, so that only very low towing speeds would be practicable, and of course the wire is expensive, costing £5,760 for the 8000 yards. This is, however, an extreme example, and itis often a practical proposition to use such cables at shallower depths. There are also applications, such as underwater television, where it would not be possible to bring the information back over an acoustic link. 16.4.2. The ‘‘Pinger’’ Though in most applications the "Pinger" is perhaps not used as a telemeter in the most conventional sense, it is a device widely used for obtaining infor- mation about equipment in the sea. It consists, in its simplest form, of a simple relaxation oscillator (Fig. 16.15) in which a capacitor is charged from a battery and discharged through a coil round a nickel "scroll" transducer using a gas tube as a switch. The pulse of current produces a momentary contraction of the ring by the magnetostriction effect and the ring then oscillates at its natural frequency, giving a damped train of waves. The circuit illustrated, using a 10- keps scroll, has a range of four miles in favorable circumstances. In this simple, free-running form, it is used by Swallow [14] in his system for deep-current measurement. He has a neutrally buoyant float which is less compressible than sea water, so that if suitably weighted it will sink to a pre- determined depth and then move around with the water at that depth. The float contains a Pinger, and is tracked using a directional hydrophone system aboard a ship. A float has been tracked for as long as six weeks in this way. NSP I 360 v BATTERY TRANSDUCER Fig. 16.15. The relaxation oscillator circuit of a "Pinger." 316 Lecture 16 A somewhat similar acoustic system working at 132 kcps has been used by Trefethen, Dudley, and Smith [15] to follow the movements of salmon. In their system, the complete transistorized transmitter is only 2.4 in. long and 0.9 in. in diameter, which is so compact that it can be fixed to the fish as a "tag" and followed from a boat using a 4-element receiving array and a servomechanism which keeps the receiver pointing at the salmon by a phase-comparison system. By controlling the repetition rate of a Pinger to precisely one per second, signals can be received and recorded on the precision echo-sounder receivers already described in Section 16.2.1. Edgerton and Cousteau [16] have used such a system for measuring the distance of a deep-sea camera from the sea floor by measuring the separation of the direct pulse from that reflected from the sea floor. Laughton [17] with his camera arranges for the pulse repetition rate ofa Pinger to change when the trigger-weight hits the sea bed and a photograph is taken. The signals are received by a hydrophone hung from the ship, and as soon as the change of rate of pinging is heard, the camera is raised a short distance, the ship is allowed to drift, and the camera is then relowered and another photo- graph taken. 16.4.3. Acoustic Telemeters with Continuous Transmission A few telemetering systems have been built inwhich the information is trans- mitted over a continuous carrier. Perhaps the type of telemeter most in demand is one which transmits the depth of a piece of equipment, usually by measuring the external water pressure. Such an instrument is in demand, for example, by commercial fishermen who are becoming increasingly interested in catching shoals of fish in midwater using midwater trawl nets. Their echo-sounders tell them the depth of the shoal as they go over it and they want to make sure that the nets they aretowing are at the samedepth. The same problem is also encountered by biologists studying the scattering layers (see Section 16.3.2), and in other applications. A successful device of this type has been described by Stephens and Shea [18]; it is based on an instrument designed by W. J. Dow. In this instrument, the pressure is made to vary the frequency of a supersonic carrier, and the tem- perature is also measured and varies an audio-frequency which is transmitted as an amplitude modulation on the carrier. The physical arrangement of the system is shownin Fig. 16.16. The acoustic transducers have to have fairly wide beams, but even some directionality greatly <— SHIP'S WAKE TELEMETER TRANSMITTER DIRECTIONAL RECEIVING / Zk TRANSDUCER Se; TRAWL CABLE MIDWATER Fig. 16.16. The arrangement in use of an acoustic telemetering depth-of-net meter. NET M. J. Tucker and A. R. Stubbs 317 improves the signal-to-noise ratio. The electrical input to the transmitting transducer is between 1 and 2 w, the frequency deviation is 21 to 36 kcps, and the audio-frequency temperature signal varies between 200 and 800 cps. The receiving transducer is slipped down the towing warp after this has been fully let out, and thus needs no extra men for its operation. After preamplifi- cation, the received signal is fed to a low frequency radio receiver whose dial reading is a measure of the depth. The output of the radio receiver is the audio- frequency temperature signal. A depth accuracy of 1% and a range of one mile is claimed for the instrument. For some purposes, suchas the seismic refraction shooting method described in Section 16.2.4 for examining sub-bottom geology, there are advantages in placing a hydrophone on the sea bed. Dow [19] has also designed an acoustic telemetering hydrophone for this application. It will receive sounds in the range 50 cps to 5 kecps and transmit these onanacoustic carrier of 21 kcps. It is capa- ble of working at depths of up to 3000 fathoms, and uses a power input to the transducer of about 30 w. 16.5. MISCELLANEOUS APPLICATIONS 16.5.1. Wave Recording An inverted echo-sounder placed on the sea bed and pointing upward at the surface may be used to record wave height. The height recorded is the distance = = — ee ft en fraction by internal waves. 318 Lecture 16 Hi bo here Saat Aa sae “ PA oo Se sees tive Fig. 16. AG Echo- sounder record showing movement of scattering layers caused by internal waves. of the transducer from the nearest part of the water surface which is effectively in the beam, which may be considerably nearerthan the water surface vertically above the transducer. Such errors can be quite large with a wide-beam trans- ducer, but if the beam is too narrow, there may be no reflecting facet in the surface area "illuminated" by the beam, and thus echoes may be lost. The other major snag with this type of instrument is that in storms, when it is probably most important to record the waves, the water is often so aerated that the sound cannot penetrate it andno echoes may be obtained for long periods of time. 16.5.2. Internal Waves Internal waves in the sea have both direct and indirect effects on underwater sound. The direct effect is refraction of sound, and this has a marked effect on asdic records (Fig. 16.17). Here, the sound is focused or dispersed so that some areas of the sea floor are more brightly "illuminated" than others and a marked pattern is produced on the record. This effect has been studied by Lee [20] and is mentioned in Lecture 8 (J. Crease), and might possibly give useful information on the waves themselves. The indirect effect is to produce movement of organ- isms in the sea which are then picked up on echo-sounders [21]. Figure 16.18, M. J. Tucker and A. R. Stubbs 319 for example, shows a scattering layer which is being carried up and down by the internal waves and allows the measurement of them at the depth of the layer. REFERENCES 1. S.T. Knott and J.B. Hersey, "Interpretation of High-Resolution Echo-Sounding Techniques and Their Use in Bathymetry, Marine Geophysics and Biology,” Deep-Sea Research, Vol. 4, 36-44 (1956). 2. A.S. Laughton, "An Interplain Deep-Sea Channel System,” Deep-Sea Research, Vol. 7, 75-78 (1960). 3. E. A. Howson and J.R. Dunn, "Directional Echo-Sounding,” J. Inst. Navigation XIV, 348-359 (1961). 4. D.G. Tucker, "Directional Echo-Sounding,” Intern. Hydrographic Rev. XX XVII, 43-53 (1960). 5. M. J. Tucker, "Beam Identification in Multiple-Beam Echo-Sounders,” Intern, Hydrographic Rev. XXXVIII, 25-32 (1961). 6. W.C. Beckmann, "Geophysical Surveying for a Channel Tunnel,” New Scientist, Vol. 7, 710-712 (1960). 7. J.B. Hersey, H.E. Edgerton, S.O. Raymond, and G. Hayward, "Sonar Uses in Oceanography,” Instru- ment Society of America, Conference Preprint 21-60, 5-9 (1960). 8. W.D. Chesterman, P.R. Clynick, and A.H. Stride, "An Acoustic Aid to Sea-Bed Survey,” Acustica, Vol. 8, 285-290 (1958). 9. M. J. Tucker and A.R. Stubbs, "Narrow-Beam Echo-Ranger for Fishery andGeological Investigations,” Brit. J. of Appl. Phys., Vol. 12, 103-110 (1961). 10. A.H. Stride, "Geological Interpretation of Asdic Records,” Intern. Hydrographic Rev. XXXVIII, 131-139 (1961). 11. R.E. Craig, "Some Successful Experiments with a Pencil-Beam Echo-Sounder,” World Fishing, Vol. 8, 40-41 (1959), 12. Kelvin and Petia "The MS 28/29 Operating and Service Manual,” Publication 342. 13. J.B. Hersey and R.H. Backus, "New Evidence that Migrating Gas Bubbles, Probably the Swim Bladders of Fish, are Largely Responsible for Scattering Layers on the Continental Rise South of New England,” Deep-Sea Research, Vol. 1, 190-191 (1954). 14, J.C. Swallow, "A Neutral-Buoyancy Float for Measuring Deep Currents,” Deep-Sea Research, Vol. 3, 74-81 (1955). 15. P.S. Trefethen, J. W. Dudley, and M.R. Smith, "Ultrasonic Tracer Follows Tagged Fish,” Electronics, Vol. 30, 156-160 (1957). 16. H. E. Edgerton and J. Y. Cousteau, "Underwater Camera Positioning by Sonar," Rev. Sci. Instr., Vol. 30, 1125-1126 (1959). 17. A.S. Laughton, "A New Deep-Sea Underwater Camera,” Deep-Sea Research, Vol. 4, 120-125 (1957). 18. F.H. Stephens and F. J. Shea, "Underwater Telemeter for Depth and Temperature,” U.S. Fish Wildlife Serv., Spec. Sci. Rept., Fisheries Ser. No. 181. 19, W. Dow, "A Telemetering Hydrophone,” Deep-Sea Research, Vol. 7, 142-147 (1960). 20. O.S. Lee, "Effect of an Internal Wave on Sound in the Ocean," J. Acoust. Soc. Am., Vol. 33, 677-681 (1961). 21. V. Valdez, "Internal Waves on an Echo-Sounder Record,” Deep-Sea Research, Vol. 7, 148 (1960). i dee wile HEE te | ul ret) fh ‘ i fs AR yy ; i a are ; heule are WO) Gaps ity Lait oe) gee ia an ree ae ey we | ar Dies tanh v LECTURE 17 SOME EXPERIMENTS ON THE REDUCTION OF STRUCTURE-BORNE NOISE J.H. Janssen Technisch Physische Dienst T.N.O. en T.H. Delft, Netherlands 17.1. INTRODUCTION "The acoustic stealth of a ship or torpedo is determined by the external noise it generates" [1]. Four different sources of underwater ship noise may be distinguished: (1) cavitation, (2) hydroelastic forces, (3) flow, and (4) machinery. This paper is concerned with some problems of machinery noise reduction. Noise control is basically a system problem. The system consists of a ship, water, and detection apparatus. It contains a source, a path, and a receiver for sound signals. The aim of noise control in this instance is to prevent detection by the enemy. In underwater noise reduction, more often than not a restriction is imposed on the measures to be taken: only the sound paths are available for blocking. It is for this reason that only the path is considered here, or rather the multiplicity of paths. Of course, not all types of ships, sources, and structures can be reviewed with respect to their acoustical behavior. A considerable simplification is obtained if only the structures of small ships like submarines Or minesweepers are studied. Only two typical noise paths seem to be important then; viz., the path via the structure only and the path via the air and the struc- ture. In the latter instance, for example, the noise is radiated by a diesel engine directly into the air and excites the shell, which in turn radiates sound into the water. The pure structure-borne noise follows the path through springs, foun- dation, and hull into the water. At large distances, hydrophones may detect the pressure fluctuations due to the radiated sound power anyway. In Fig. 17.1 a noise path together with associated levels is illustrated. In this paper some experiments, both theoretical and practical, relating to the steps in the path (machinery to foundation, foundationto shell, and shell to water) will be discussed. 17.2. UNITS AND LEVELS Sound power manifests itself by way of fluctuations in pressure and particle velocity. In fluids and gases, these pressure fluctuations are easily measured 321 322 Lecture 17 machiner y foundation distance O1 10 kHz O1 10 10kHzO01 10 OkHzO1 10 10kHz0 102 102m eS aT —we— § —— mf ——!sf ——e kHz Fig, 17.5. For “normal” excitation, two isolation curves were determined: (A) exciter position in the middle of a steel bar resting on two rubber blocks on a 4-m I-NP-16-beam, and (B) exciter position above one of the rubber blocks. From the stiffness of the blocks (~2.5° 10* N/m per block) and the impedance level of the beam (L,,, shown in figure), an approximate isolation curve may be computed which agrees fairly well with curve A. The exciter position clearly influences the experimental result; additional rotation of a spring contact plane presumably increases the velocity level L,, of the beam. Sinusoidal plane waves may exist in the plate or beam. For the bending wave velocity cg one finds that cp =V27 fc, ty (13) where c, =\VE/p, the longitudinal plane wave velocity in the material; and 1, is the so-called radius of gyration, equal to \I/A. For plates, this radius of gyra- tion is given by i, -—4 (14) where h is the plate thickness; for beams, i, may be found in tables or hand- books. In Fig. 17.6 the bending wavelength \g=c,/f is shown as a function of the frequency f and the plate thickness A for three common building materials, The longitudinal wavelength for sinusoidal plane waves in air and in sea water is also shown. For the greater part of the audio-frequency range, A, is smaller than A in sea water. This fact has an important bearing on the sound radiation by shell plates into water, and itcanbe understood in a qualitative way as follows. Suppose two loudspeakers are mounted close together inone baffle. They vibrate in opposite phase. If the distance between the speakers is less than the wave- length in the surrounding air, the sound radiation is very inefficient because of 328 Lecture 17 10.0m plate ehiekne os 0 wavelengths for longitudinal x Re waves in air or in seawater 40 equiv. beam th. and Xp for bendingwaves in steel or aluminium plates h(m) d ~_ (thickness h) or beams (equiv. 20 (e) ~ > th. hL for wood actual aN is 10 % smaller 1.00m ; SS SN Php 0.40 = SS Sle 0.20 my (B) 010m = 5000 m/s for steel, aluminium an = 4000 m/s for wood = VI/A (radius of gyration of cross section) 0.040 = h/2V3 for plates 20 = 3.46 iy for beams SS 0.01m 1 2 4 8 i) €2 (sS 2S Aso) Soo) | 2 4 8 iS s2 3) ——_ Hz kHz Fig. 17.6. Wavelengths for longitudinal waves in air or in sea water and for bending waves in plates of thickness h; some equivalent I-beam DIN-numbers are indicated. The lines for constant A must not be extended to the right. the "pumping-around" effect. A similar situation exists when the bending waves in a plate are of such a form that nearby parts of the plate vibrate in opposite directions within a distance of, say, halfthe wavelength associated with the sound radiated into the surrounding fluid medium. The frequency f,, for which cg =c, is called the critical frequency; here c, is the velocity for longitudinal waves in the fluid. The critical frequency is given by Cw for = 2ncpi, (15) as may easily be derived. For frequencies f>f.,, the radiation is very efficient and shows pronounced directional effects. The frequency range discussed in this paper is such that Ag < 2m, approximately, for the lower limit; and f alAYO LAD The meaning of the various symbols is explained below. As is usual, the real part of the complex v(C) is the measurable quantity, "velocity at C." The numerator of Eq. (17) contains only the ratio of the values at C and A of the vth natural mode. This ratio is equal to ¢,(C)/¢,(A), where ¢, is the characteristic function describing a natural mode. With the aid of tables of these functions [11] this ratio can be determined. In the denominator of Eq. (17), the so-called "quadratic amplitude transform factors" q,(A) are given by R32 up 02(A) bo. qv(A) = (18) This name suggests the same action so weil known from electric transformers. These impedances are transformed in the ratio 1 to n”, while currents or volt- ages are transformed in the ratio 1 to n. In q,(A), a more general seesaw action is described: the mechanical impedance felt by an exciting force at one end of a seesaw due to a load at the other end is proportional to the square of the ratio of the distance load-pivot to the distance force-pivot. The bar over 4? indicates the mean value over the homogeneous beam of @ squared. In [11], the charac- teristic functions are normalized in such a way that 330 Lecture 17 2) a pote eat avtA)= (ay @3(A) 8) thus allowing a quick determination of q,(A). The factor 9,(A) in the denominator of Eq. (17) may be called a force dis- tribution factor. It is equal to 1 for a point force applied in A. For a pressure distribution, it is given by a, (A)F A\ a ae Pv(A) 7p, as (20) where F is the amplitude of the total force [cf. Eq. (16)]. For the ratio @,/,(A) under the integral sign, ¢,/¢,(A) may be substituted (cf. [11]). The last term inthe denominator of (17) is the most illustrative. It is given by 2 M Zy=joM +R,+ = R,(1 + jv,Q,) (21) the well-known expression for the complex impedance of a series circuit, where Ry =2n at (22) Ov=—t (23) ee ary (24) Aline fa and 7 is the loss factor, f, is the vth natural frequency, f is the excitation fre- quency (@/27), and M is the total mass of the beam. Eventually, Eq. (17) turns out to be a complicated expression for what may be called a "parallel connection v(A) | F(A) AS \S “YS \ XX ~ SQ YOO YS AL WN ni SSAA OO SOY SYS . SX WV’ >» WS esa= Fig. 17.7. Hydraulic analog of a mechanical structure (e.g., beam or plate) excited by a sinusoidal point force F(A). The velocity v(A) at A depends upon the response of infinitely many "resonators" (mass on spring and mechanical resistance) numbered 1,2,3,...%. An electrical analog would be a parallel connection of series circuits. The values of the circuit components are given in Eqs. (17) through (24). J.H. Janssen 331 of series circuits." The natural frequencies of the beam correspond to the "resonant frequencies" of the series circuits. A hydraulic analog for a point- force excitation is shown in Fig. 17.7. The picture of "parallel connection of series circuits" for a beam seems to have a general validity for other mechan- ical structures as well. It agrees very well with experimentally observed reso- nance curves of mechanical structures which closely resemble those of the simple classic RLC series circuit. The behavior of these circuits is well known, and the noise impedance Z,,, if measured with half-octave band filters, is given by (25) where the symbols of Eqs. (7), (22), and (23) are used. Of course, Eq. (25) can be only approximately valid for a mechanical structure and only for one reso- nant frequency within the frequency band of the exciting force noise. Assuming the various natural frequencies within a given frequency band to be sufficiently separated, it is possible to derive an expression for the noise impedance of a plate or a beam as soon asthetotal number of the "peaks" in that band is known. For simply supported beams or plates, the noise impedances averaged over the beam or plate turn out to be given by Ss Mcph Zieh = On ONT ae (26) for point excitation of a rectangular plate of thickness h, width 5, and area S = 1b; and, al 2 GB gf (27) for line excitation along the width b of a plate; and, al M2 Vc 1 GE ce Og (28) for point excitation of a beam (length / and radius of gyration i,). In Fig. 17.8 the reasonable agreement between a measured and the corresponding computed impedance from Eq. (26) is shown. Especially interesting is the deviation from the theoretical curve for frequencies f > f.,. Presumably it is due to the increased load caused by the efficient radiation of sound into the surrounding air; the order of magnitude for this effect is correct. A closer examination of the results given above raises at least two questions respecting their applicability to underwater noise control. Up to now, theory has introduced only structural data, but no coupling of the structure with a fluid medium. The first question, therefore, concerns the extra load due to water when in direct contact with a vibrating plate. The second has to do with the excitation. It was assumed that the exciting force acted in a direction parallel to the resulting velocity of the points on the beam. In principle, it must be pos- sible to handle situations like that shown in Fig. 17.5 with the aid of the method given. However, it is too simple a supposition that a diesel engine vibrates in a "normal" direction only. It is equally probable that its contact planes with springs move "parallel" to the beam, or otherwise, of course. 332 Lecture 17 steel plate 2.5mm 110 n= 0.015 90 @ Oo o (e) ———_=— impedance level (L,) uO {e) 40 ] 2 4 8 lie 2 ©3 125 250 Sco) jl 2 4 8 le 32 es Sao ii Hz kHz Fig. 17.8. Point-impedance level as measured (average of three points as shown; half-octave-band noise) on a steel plate bolted to a steel doorframe in wall of reverberant room (156.3 m*, empty; reverberation time approximately two sec). The measured values are connected, For comparison with theory, a curve is shown (heavy line), computed according to Eq. (26) and using measured 7-values (derived from reverber- ation times of plate; 7 = 2.2/Tf,). A solution to the first problem can be estimated as long as f- + +>1Xawrs 2X1 + + + 2Xawrs «> mXi» ++ «mX2wr) where ,x; is the pressure at the th space sampling point and th time sampling point. Both f,,(X) and f,(X) have to do with the joint occurrence of the 2WT'M samples (;x,,...,,,xX2wr) in space—time. Under certain conditions [Eq. (2)], 1(X) is separable into space and time components; generally, it is not. Substitution of the specific probability density functions into Eq. (7) gives the specific processor design for efficient detection. This is done in the next section for one space—time and two space-only examples. While this is the pri- mary application of the space—time likelihood ratio, a second and equally inter- esting use of the likelihood ratio is as a gauge of the efficiency of existing or proposed processors, or of the effect of different states of knowledge upon the capability to make accurate or, more generally, minimum average risk descriptions. 344 Lecture 18 faa) a Fig. 18.1. Receiver; operating characteristic curve. fe) =| p(FA) Let us imagine many independent successive trials using the detection likelihood-ratio processor in the f,,{X) and {,(X) acoustic fields. The (a priori) probability of occurrence of SN isp(SN), and p(W) is the a priori probability of occurrence of Non any trial. Athresholdconstant K is compared with the likeli- hood-ratio processor output at each trial. If the processor output exceeds K , the decision SV is made (5sy); otherwise, the decision N is made(6,). There are four possible combinations of event SW or W and decision 5, or dy: (SV, dsy) = detection (D) (SV, dy) = miss (WV, 6sy) = false alarm (FA) (VN, dy) = correct dismissal If p(D) =p(SN, dsy) is the probability of detection developed as the number of trials becomes infinite, and p(FA) is the probability of false alarm similarly developed, then it is found that both are functions of K. If K is large, both p(D) and p(FA) are small; if K is small, both p(D) and p(FA) are large. Generally, if K is varied, a receiver operating characteristic will be traced out for a given f,(X) and f(x), as shown in Fig. 18.1. If £,(X) or fy(X) is changed, a family of operating characteristics will be generated. Further, if some processor other than /(X) is used in the trials, a different p(D) and p(FA) will result, and will be to the right and below the operat- ing characteristic; i.e., the processor is not as efficient as I(X). From this brief discussion of operating characteristics, the mechanism for comparing different states of knowledge and/or different processors in terms of p(D) and p(FA) should be clear. A fuller discussion of the use of operating characteristic curves and receiver efficiency is given in [1]. 18.3.3.1.Examples Three examples will be given: I. Signal is known exactly in time and space (waveform and wavefront); P. L. Stocklin 345 additive Gaussian noise is independent between sampling points in space and between sampling points in time. Il. (space only): Signal is known exactly in space. Noise is additive and Gauss—Markov between space sampling points. III. (space only): Signal wavefront is Gauss—Markov perturbed between space sampling points; noise is Gauss—Markoy between space sampling points. Example I: Suppose there are M hydrophones receiving either (a) a signal S known exactly in time and space plus independent Gaussian (in time and space) noise, or (b) the noise alone. What is the optimum space—time processor? If iXj is the input acoustic pressure amplitude at the ith hydrophone at the jth instant of time, i$; is the signal pressure amplitude of the jth hydrophone at the jth instant of time, and X= (iki, 1X2,-+-) 1X2wrs---3 mX1y +++) mX own) (8) then 3 1 ou 21a fy(X) = Qnoy)-™"7 exp (-—5 >) axy (9) _ 2on j=l fal and y 1 M 2WT fsy(X) = (2r0y) "7 exp |~ —> De (ix; — ,s;)? (10) 2on fz1 j=l where f,(X) is the probability that if noise alone is present then sample X =(1%1,---,yX2wr)Will occur; and f,,(X) is the same for signal-plus-noise con- dition. The space--time likelihood ratio for this example,/:(X), is _fsn (X) LS a 2 1 hQ) = mo | dee x > Gsy = 21015) a In Eq. (11), we see that a. The basic processing operation is a space—time cross-correlation be- tween the signal known exactly ;s, and the input ix,, since the double summation over ,s; is just the total signal energy received at all the hydrophones, and so is a constant known exactly. b. It is immaterial whether the space summation (usually called "integra- tion") is done first. c. By "signal known exactly in space" we mean that we know the wavefront location. Thus, our signal-known-exactly assumption means that we know both the waveform and the wavefront. Two completely equivalent block diagrams for Eq. (11) are given in Fig. 18.2. As a final point, the ROC curve for this example is identical to Fig. 2 of [1], with 2ME No ale where E is the signal energy as measured at one hydrophone output. The spatial 346 Lecture 18 GRATION BEAM FORM J | THRESHOLD THRESHOLD Fig. 18.2. Example I, space—time processor. processing gain in db, then, is 10 log M for this case, and the temporal process- ing gain is 10 log (2E/No). Example II: The following example is restricted to space statistics only, to bring out the idea that for several quite likely statistical situations pattern formation in the usual sense is not optimum likelihood-ratio processing in space. This example illustrates the departure from pattern formation due to a space-correlated noise field, specifically, a first-order Gauss—Markov noise field. In this example, a particular instant of time is chosen and space statistics only will be discussed. For the noise field alone, with M (regularly spaced) point hydrophones, the Mth-order spatial-probability distribution function f,(X) is, under the Markovian assumption, fy(X1) = fwGixa- ++) m1) = fy (1X1) + fy, 1x1 (2¥1) fy, yx, (3%1) +**five m—1%1 (1) M fy(X1) = fy(x1) pun fy, pax 4X1) (12) and together with the Gaussian assumption, Eq. (12), gives 2 M 2 BG ell ral lee ale eg ex) |e (oS ews (13) 2oy f22 2(1-pron where o, is the noise power per hydrophone, and py is the normalized noise (spatial) correlation function between adjacent hydrophones. Now, if signal is known exactly—in this example, such a state of knowledge means knowing the signal wavefront at the chosen instant of time—then fsy(X) is | x1 = 181) a yes — $1) — py(i-1x4+ y= 181)? faw(X1) = (2a 1-™/? [1 — pZ1--Y/? exp .— w(X1) = [2no% PN P 2oz, a 2(1- prow Using Eqs. (7), (13), and (14): = fy (X) a 1 2 2 ba 2 y2 In(X1) = Fy = “lors -(1- py) st - > GS1— Pw -i-181) 72a Pw) 1X1-181 M M + 2 yX1.mS1 +2(1+ py) D> X1181 + 2 py DY Gx1s-181 + veel (15) i=2 i=2 P.L. Stocklin 347 eH @ Fig. 18.3. Spatial likelihood-ratio processor for Gauss—Markov (spatial) possibility distribution of noise of Example III. Dotted lines enclose processing due to spatially correlated noise. The first two additive terms on the right of Eq. (15) are signal-bias terms. The next three additive terms are those for normal pattern formation [see Example I, Eq. (11)]; however, the coefficients of the pattern terms for inputs ,x, and mx, differ from the coefficient (1+ py) for the majority of the inputs. Finally, additional processing of the inputs beyond pattern formation is indicated by the last additive term. The spatial likelihood-ratio processor design for this ex- ample is drawn in Fig. 18.3. Comparing Figs. 18.2 and 18.3, we see thatthe essential difference in spatial processing due to spatially correlated noise (Example II) versus independent noise (Example I) is the multiplication of an input by both the succeeding and following values of the signal. For a plane wavefront, this operation would con- sist of delaying and advancing an input fromthe ith hydrophone as though it were received at the (s;-1)th and(@+1)th hydrophones, respectively. If we allow the noise to become spatially independent, p, goes to zero and the Markovian proc- essing vanishes. Example III: The previous example may be generalized to include first-order Gauss—Markov perturbation of the signal wavefront about its ideal mean, in addition to first-order Gauss—Markov noise in space. The spatial likelihood- ratio processor design for several interior (i 41,M) hydrophone outputs is given in Fig. 18.4, together with the values of the amplification coefficient in Table I. Comparison with Fig. 18.3 reveals two new processes: multiplication of hydro- phone outputs and squaring of the individual hydrophone outputs. By juggling values of 0,, py, o&, and of, a smooth transition from the case of classic pat- tern formation alone (Example I), through correlated noise processing (Ex- ample II), to completely incoherent spatial processing can be found. This latter 348 Lecture 18 Fig. 18.4. Space processor for Gauss—Markov perturbed signal wavefront inGauss— Markov noise. case corresponds to the conditions p,=0=p, and of >oy,. As an intermediate example, for p,=1, py =0, and o2 = oy, the amplification factors become: In Table 18.1, values of the amplification factors for the processor of Fig. 4 are given, where Ps = normalized correlation of signal perturbations between adjacent hy- drophones py = normalized noise correlation between hydrophones a= power of signal perturbations oy = Noise power at one hydrophone oy = of + on _ Pss + won RiSNi- pasos sone Os + On In these examples, previously developed space and time processing, such as pattern formation and cross correlation, have been related to novel space proc- essing through inclusion in the general framework of space—time decision theory. The purpose of these few examples is to suggest the utility of this framework as a logically developed and heuristic guide to processor design and efficiency—that is, to space—time processor research. P. L. Stocklin 349 Table 18.1. List of Values of Amplification Factors for Spatial Likelihood-Ratio Processor of Fig. 18.4 Process amplified Squaring of individual hydrophone outputs, followed by summation— essentially, spatial incoherent processing (1 + pew) », Os pn) 208n(1— psy) 20 (1 - py) Classic pattern formation—essen- 2 pee SNe tially, spatial coherent processing oSn (1 — psy) Pair-wide multiplication of hydro- phone outputs—related to un-nor- malized interhydrophone correla - tion of signal perturbations aE ea ee ee os (1—psn) on (1 - pp) Offset pattern formation—related to both noise and signal interele- ment hydrophone correlations 2 Psn. 2 oSn (1 — psy) REFERENCES 1, W.W. Peterson, T.G. Birdsall, and W.C. Fox, "The Theory of Signal Detectability,"” Trans. IRE, PGIT- 4, 171 (September, 1954). 2. P.L. Stocklin, "Limits of Measurement of Acoustic Wave Fields," manuscript submitted for publication, J. Acoust. Soc. Am. 3. D. Van Meter and D. Middleton, "Detection and Extraction of Signals in Noise from the Point of View of Statistical Decision Theory. Part I," J. Soc. Ind. Appl. Math., Vol. 3, No. 4, 241 (December, 1955). Jee ns) Bey ORR eA. Be ‘ 1 ROL ae tO TOSheDRyA of eR hoot ORR a TON) teas | I ns aco eelahrh leche eee elem cmamemdcnartibe: Welt 1 TW Leelee eastern catinaaamena ia i eer or ohare aire aha nD i ea ; 4,6 ahi ket C ares et ar aki th oemoadia — apnea cet 1 ben cular Ny Maes Nee et ean. } 43 Cont) tye Cues 412) Pevnaitoe .eoiay tie i wane! YO maine te af 1 ; ‘ aks we SCA Lipper) sass | VIS Rae ’ wee he a Sh LONE ry : { eee ot eo at ft =) iis OMA Ove ant 1) ee | Pu; 1 \ oe yet 4 JRA DY PR GY BRL ASIGRSD eT REAR AR { fiesd : are vere ty ws a Rov ear 9500 Shay ; om Hae ‘ Awe - i! ced Bing k »oanoibvdven) Hexion iy ws ( A iv = eirorn ay Ttety bare dy Gales, Vinie a RN sal het? YORE SEE ay rets meek simi Copyphe bo aoe hdd oat Wee sogihyoibys fh be GA Atrep oy Mowe : Pate hin " j dy 8 td ceeed eee i Tae A malonate t Yoatetl” equa feted AP Dan ROLE vielirra ay Sh 147 MONE Ge a a t i —— Ty ' ; f i "| i ‘ I % i 4 4 Le (eu \) : LU 1 F ABR ' ev ; 7 ; ds. RED Na i ‘ a i ey : h ie ‘ i 4) we } t eo ae . ee ‘ ft Thr an ff) i ; ' ike u tin u) [ ‘ APPENDIX: ATTENDANCE AT THE INSTITUTE Professor Vernon M. Albers Chairman of the Institute Ordnance Research Laboratory The Pennsylvania State University University Park, Pennsylvania, U.S.A. Mr. Homer R. Baker North Atlantic Treaty Organization Scientific Affairs Division Paris, France Dr. D. Schofield Naval Research Establishment Halifax, Nova Scotia, Canada Professor D. G. Tucker University of Birmingham Birmingham, Warwickshire, England Dr. D. E. Weston Admiralty Research Laboratory Teddington, Middlesex, England Dr. G.G. Parfitt Department of Physics Imperial College of Science and Technology London University London S. W. 7, England Dr. Martin Greenspan National Bureau of Standards Washington, D.C., U.S.A. Dr. C.C.A.N. Fodche Laboratoire de Detection Le Brusc, (Var.) France Dr. James Crease National Institute of Oceanography Wormley, Surrey, England Professor Erwin Meyer Ill. Physikalisches Institut der Universitat Gottingen Gottingen, West Germany Mr. Carl J. Anderson Norwegian Defense Research Establishment Horten, Norway Mr. Arne Aubell Norwegian Defense Research Establishment Horten, Norway Lecturers Participants 351 Dr. R. W. B. Stephens Co-Chairman of the Institute Department of Physics Imperial College of Science and Technology London University London S. W. 7, England Dr. A. B. Wood Admiralty Research Laboratory Teddington, Midciesex, England Dr. H. Wysor Marsh Marine Electronics Office Avco Corporation New London, Connecticut, U.S.A. Professor Eugen J. Skudrzyk Ordnance Research Laboratory The Pennsylvania State University University Park, Pennsylvania, U.S.A. Professor Paul M. Kendig Ordnance Research Laboratory The Pennsylvania State University University Park, Pennsylvania, U.S.A. Professor E. J. Richards University of Southampton Southampton, Hants, England Mr. M. J. Tucker National Institute of Oceanography Wormley, Surrey, England Mr. A. R. Stubbs National Institute of Oceanography Wormley, Surrey, England Ir. J.H. Janssen Technisch Physiche Dienst T.N.O. en T.H. Stieltjesweg 1 Delft, Netherlands Mr. P. L. Stocklin Office of Naval Research Washington 25, D.C., U.S.A. Mr. G. J. Barber Admiralty Underwater Weapons Establishment Portland, Dorset, England Professor A. Barone Instituto Nazionale di Ultracustica Rome, Italy 352 Professor J. F.W. Bell Royal Naval College Greenwich, England Mr. G.C. Braysher Admiralty Underwater Weapons Establishment Portland, Dorset, England Dr. A. E. Brown Kings College Durham University Newcastle upon Tyne, England Mr. S. Byard Admiralty Research Laboratory Teddington, Middlesex, England Mr. I. J. Campbell Admiralty Underwater Weapons Establishment Portland, Dorset, England Dr. H. Charnock SACIANT ASW Research Center La Spezia, Italy Mr. B. M. Cheney Society Alsacienne de Constructions Mecaniques 69 Rue de Monceau Paris, France Mr. R.C.R. Chesters Marine Equipment Unit Plessey Limited Ilford, Essex, England Mr. W. B. Coffman Office of the U.S. Naval Attache London, England Mr. R. P. Coghlan Admiralty Research Laboratory Teddington, Middlesex, England Mr. G. L. Connon Admiralty Underwater Weapons Establishment Portland, Dorset, England Mr. M. J. Daintith Admiralty Underwater Weapons Establishment Portland, Dorset, England Dr. F.T. Dietz Physics Department University of Rhode Island Kingston, Rhode Island, U.S.A. Dr. W.N. English Pacific Naval Laboratory Esquimalt, British Columbia, Canada Professor Dr. Maurizio Federici Viale Vittorio, 14 Milan, Italy Mr. R.D. Finch Department of Physics Imperial College of Science and Technology London University London S. W. 7, England Dr. F.M.V. Flint Admiralty Underwater Weapons Establishment Portland, Dorset, England Appendix Mr. J.H. Foxwell Admiralty Underwater Weapons Establishment Portland, Dorset, England Mr. A. Freedman Admiralty Underwater Weapons Establishment Portland, Dorset, England Mr. I. A. Gatenby Admiralty Underwater Weapons Establishment Portland, Dorset, England Mr. W. K. Grimley Admiralty Underwater Weapons Establishment Portland, Dorset, England Mr. Harold Haegermark Stockholm, Sweden Dr. G. K. Hartman Naval Ordnance Laboratory White Oak, Silver Spring, Maryland, U.S.A. Mr. A. Hobson Admiralty Research Laboratory Teddington, Middlesex, England Mr. G. P. Horton Admiralty Underwater Weapons Establishment Portland, Dorset, England Mr. S.D. Hawkins Department of Physics Imperial College of Science and Technology London University London S. W. 7, England Mr. Hub Royal Naval College Greenwich, England Mr, L. Kay Birmingham University Birmingham, Warwickshire, England Mr, A. L. Kendrick Admiralty Research Laboratory Teddington, Middlesex, England Dr. T.S. Korn Faculte des Sciences Appliquees Ecole Polytechnique Universite Libre de Bruxelles Ave. F.D. Roosevelt 50, Bruxelles, Belgium Mr. R. L. Laval SACIANT ASW Research Center La Spezia, Italy Mr. D.R. Leah Admiralty Bath, Somerset, England Dr. E. Rune Lindgren Tekniska Hogskolan Stockholm, Sweden : (Visiting Professor, Johns Hopkins University, Baltimore, Maryland, U.S.A.) Mr. D.A,. Linkens Marine Equipment Unit Plessey Limited Ilford, Essex, England Appendix Mr. J.R. Littlefair Admiralty Research Laboratory Teddington, Middlesex, England Mr. B. W. Lythall Admiralty Underwater Weapons Establishment Portland, Dorset, England Mr. H.H. Margary Admiralty Research Laboratory Teddington, Middlesex, England Dr. H. Medwin U.S. Office of Naval Research London Branch Keysign House London, England Dr. J.H. Mole Admiralty Underwater Weapons Establishment Portland, Dorset, England Mr. A. Nairn Admiralty Underwater Weapons Establishment Portland, Dorset, England Mr. G. W. B. Neal Admiralty Underwater Weapons Establishment Portland, Dorset, England Mr. E. Neppiras Mullard Limited London, England Mr. R. B. Newman Admiralty Underwater Weapons Establishment Portland, Dorset, England Mr. T. O'Brien H. M. Admiralty London, England Mr. Aubrey Pryce Office of Naval Research Washington 25, D.C., U.S.A. Mr. E.D. Rabun Bureau of Naval Weapons Washington 25, D.C., U.S.A. Mr. J. W. Ramsey Admiralty Bath, Somerset, England Mr. J.D. Rands Department of Physics Imperial College of Science and Technology London University London S, W. 7, England Professor R. E.H. Rasmussen Tekniske Hgjskole Pstervoldgade 10 Kobenhavn K, Denmark Mr. Charles Reis Research Consultant Hewlett-Packard Company 1501 Page Mill Road Palo Alto, California, U.S.A. Mr. R. W. Renson Admiralty Underwater Weapons Establishment Portland, Dorset, England 353 Mr. T.N. Reynolds Admiralty Underwater Weapons Establishment Portland, Dorset, England Mr. H, Ritter Admiralty Research Laboratory Teddington, Middlesex, England Lta. (I) G. Rittore Italian Navy Mariperman La Spezia, Italy Mr. A. Y. Robin Society Alsacienne de Constructions Mecaniques 69 Rue de Monceau Paris, France Dr. A. Roshko U.S. Office of Naval Research London Branch Keysign House London, England Mr. J.S.M. Rusby Admiralty Research Laboratory Teddington, Middlesex, England Mr. D.L. Ryall Admiralty Research Laboratory Teddington, Middlesex, England Ir. H.A. J. Rynja Physics Laboratory National Defence Research Council The Hague, Netherlands Mr. J. Sands Royal Naval College Greenwich, England Dr. Sauls Royal Naval College Greenwich, England Dr. Daniele Sette Department of Engineering University of Rome Rome, Italy Mr. Stig Sdderqvist A.B. Akustikbyran Atterbomsvagen 50 Stockholm, Sweden Dr. D. Stansfield Admiralty Underwater Weapons Establishment Portland, Dorset, England Mr. H. Sussman U.S. Navy Underwater Sound Laboratory Fort Trumbull New London, Connecticut, U.S.A. Professor G. B. Thurston Department of Physics College of Arts and Sciences Oklahoma State University Stillwater, Oklahoma, U.S.A. Dr. W.C. Thompson U.S. Office of Naval Research London Branch Keysign House London, England 354 Commander Trendell Royal Naval College Greenwich, England Dr. J. Tunstead Admiralty Underwater Weapons Establishment Portland, Dorset, England Mr. G. Voglis Admiralty London, England Dr. R. V. Waterhouse Airo, England Dr. H.H. Waterman SACIANT ASW Research Center La Spezia, Italy Mr. A.G.D. Watson Admiralty Research Laboratory Teddington, Middlesex, England Mr. B.S. Webster Department of Physics Imperial College of Science and Technology London University London S. W. 7, England Appendix Dr. V.G. Welsby Birmingham University Birmingham, Warwickshire, England Dr. S. Wennerbery Stockholm, Sweden Dr. M.A. Williamson Dean, College of Engineering and Architecture The Pennsylvania State University University Park, Pennsylvania, U.S.A. Mr. Willis Department of Aeronautical Engineering Southampton University Southampton, Hants, England Mr. R. W. Windley National Research Department Corporation 1 Tilney Street London W. 1, England Mr. Jan Zeibon Navalkonsult Orlogsvarvet Stockholm 100, Sweden La Lik ei fe ~~ E Pas Bae re Sener k ab vasee iS Stag Ds means ise M ¢ ot § . BS Ge See a ¥ 2 oe 5 ee Ps Poth *) atone ere! Sy ab : Siti seh Seine ane By aa ties SPS Ce Res nt Mats ,> ae fetta dey ie